Questions on quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

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1answer
25 views

Why does this hyperboloid change into a surface?

Given this equation $x^2+y^2+z^2+2xy+2xz+2yz-x-y-z=6$ and the corresponding quadric: If I rearrange the equation to $(x+y+z-3)(x+y+z+2)=0$ (which is equivalent), I get: So, which is the right ...
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0answers
20 views

Proving that a line is a tangent to a quadratic curve [on hold]

Show that the line $y = x - 3$ is a tangent to the curve $y = x^2 - 5x +6$ I have no idea where to start.
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2answers
37 views

What type of equation is this? How to solve it?

$$m^4+a^4=0$$ , the answer I obtained is $$0+i1,0-i1$$ but the answer is given as a/sqrt(2)-a/sqrt(2),a/sqrt(2)+a/sqrt(2)
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1answer
38 views

solving the equation by reducing it to quadratic form

Solve for $x$ $$4^x-\dfrac{3^x}{\sqrt3}=3^x\cdot\sqrt3-\dfrac{2^{2x}}2$$ I don't understand how to convert it into quadratic equation how should I equate all bases
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2answers
47 views

Alternative Quadratic Formula

Well the formula for solving a Quadratic equation is : $$\text{If }\space ax^2+bx+c=0$$ then $$x=\dfrac{-b \pm \sqrt{b^2 -4ac} }{2a}$$ But looking at this : [Wolfram Mathworld] (And also in other ...
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1answer
30 views

Using a number system other than the decimal [duplicate]

Travelling in the Kingdom of Crystal Skull, Indiana Jones discovered a small box with notation $$ 3 x^2 - 25 x + 66 = 0 \implies x_1 = 4,\; x_2 = 9, $$ which seems to be incorrect. However after ...
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2answers
26 views

Quadratic equations / Perfect square

I am dealing with a programming problem and was wondering if there's a general method to solve it. Is there a general way to find 'n' such that: $a^2n^2 + bn - c$ is a perfect square? a, b, c given ...
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0answers
21 views

Find Next Position and Velocity from Instantaneous Values

To find the position of an object at a given point in time: $y_0 + v_0t - \frac{32t^2}{2} = y_t$. And to find the object's speed at a given point in time: $v_0 - 32t = v_t$ So say I give the ...
1
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2answers
51 views

Why $ax^2+bx+c = a(x-r)(x-s)$, where $r$, $s$ are the roots?

When I was reading about math, I came across the following - Suppose the roots of the quadratic $ax^2+bx+c$ are $r$ and $s$. Then $ax^2+bx+c = a(x-r)(x-s)$ for all values of $x$. Is there ...
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0answers
15 views

Suggestion for a good book/ebook [on hold]

I need to study Quadratic Equation and Parabola and their relation. Can anybody suggest me a good book/ebook. Thank you for help.
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0answers
42 views

What is the relationship between these numbers? [closed]

Please would you help with this? Thank you in advance. Numbers are grouped into 3 inputs, giving 3 outputs. I am trying to establish the connection between the numbers. Each group of 3 appears to ...
2
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2answers
92 views

My brother asked me to explain a algebra problem. How should I explain it?

So the problem is: $$\frac{4}{x}+\frac{6}{2}=x$$ And we solved it using the pq formula. But than he asked me: How do I know when I should apply pq to similar equations like this and not just: ...
5
votes
3answers
609 views

Solution to quadratic question of the form 0/0

What are the possible values of $x$ for the following equation: $$\frac{x - 1}{1 - x} = \frac1x$$ This equation is equivalent to $$x^2 - 1 = 0$$ which factors to $1, -1$. However, is $1$ the ...
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1answer
48 views

Are these three equations equivalent? [closed]

I'm trying to figure it out quite some time now, but I can't seem to transform these equations into one another. ...
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4answers
43 views

Find $f(a)$, $f(a + h)$, and the difference quotient, given $f(x)=7-8x+2x^2$

Question is here: I need help with part c. I tried plugging everything in and simplifying to a point where my final answer was $(-8h+2ah+2h^2)/h$ My work: $(7-8a-8h+2(a+h)^2-7+8a-2a^2)/h$ ...
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0answers
17 views

Differential Equations: Confocal Ellipse and Hyperbola

I am currently brushing up on Conic Sections, and I am having some problems on solving a first order quadratic differential equation. I would appreciate any help on the topic! I know that confocal ...
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5answers
73 views

Could translate/explain this for me?

I have this problem: $$ 10x^2 - 7x - 12 = 0 $$ And apparently the method to factoring it is to find two numbers whose product is the same as the product of the coefficient of $x^2$ and the constant ...
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1answer
30 views

Quadratic Equation/Translation [closed]

Everyone here, please can you help me to translate these problems into a quadratic equations? Edna paid at least 1200 for a pair of pants & blouse. The cost of the pair of pants is 600 more than ...
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0answers
30 views

Problem Solving/Quadratic Equation [closed]

Can you answer these? I need help. Note: (Please I also need a solvings for every equation) Edna paid at least 1200 for a pair of pants & blouse. The cost of the pair of pants is 600 more than ...
3
votes
1answer
31 views

Find the number of equations having real roots.

If both $a$ and $b$ belong to the set $\{1,2,3,4\}$ , then number of equations of the form $ ax^2+bx+1=0$ having real roots is $a.)\ 10\\ \color{green}{b.)\ 7}\\ c.)\ 6\\ d.)\ 12\\ $ To solve ...
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1answer
36 views

not easily factored quadratic expression how to find its roots [closed]

Could you please help me and explain this issue: If a quadratic equation is not easily factored then its roots can be found using quadratic formula: If $ax^2+bx+c=0$ ($a\ne0$), then the roots are ...
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5answers
89 views

Sum of real solutions on equation $\sqrt{\sin^2{x} + {1 \over 2}} + \sqrt{\cos^2{x} + {1 \over 2}} = 2$ in interval $[0,2\pi]$ is?

I know that solution is $4\pi$ but I do not know how do they get to this solution. I always get that $x \in R$ and that $-1 < \cos 2x < 1$ when converting it to double angle. EDIT : So ok, I ...
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1answer
50 views

$ a + a^2 = 90 $. Need hint.

From trig text. Am supposed to find complementary angles $a$ and $a^2$. Tried completing the square, got $(a + 1/2)^2 = 361/4$. Stuck. Help.
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2answers
43 views

Quadratic question problem

I have been asked to look at a yr 12 question about a space ships trajectory modelled by a quadratic equation. But my solution to the question has a negative minimum for distance at a time of T = 13 ...
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5answers
56 views

How to find value of $c$ in $ax^2+bx+c=0$ having the $a$ and $b$?

Problem: solve (find roots): $ 7x^2-3x=0$. How to find $c$ in order to solve using the Quadratic Formula?
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7answers
67 views

How to factor $ax^{2}+bxy+cy^{2},\,a\neq 0$?

Question: Factor: $3x^{2}-5xy-12y^{2}$ Answer: $(x-3y)(3x+4y)$ What are the exact steps to finding this answer from the original question (factored form from standard form, respectively)?
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2answers
22 views

Higher Order Polynomial Function Solver

I have a 5th order, uni-variable, polynomial :( As I understand the only way to solve this is to guess? Since this is a real world equation, rather than something from a textbook, there really isn't ...
1
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2answers
34 views

Proof for showing $1 + \frac{c}{a} + \frac{b}{a} > 0$ for any quadratic equation,where its roots are non real.

The question is as follows : If the equation $ax^2 + bx + c$ has non real roots, prove that $1 + c/a + b/a > 0 $. Looking at the question,the first thing that came to my mind was to use ...
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2answers
48 views

finding maxima and minima of a quadratic equation

I'm dealing with a quadratic equation(with 2 independent variable) which looks like: $$f(x,y) = 15.390x^2 - 0.001y^2 - 0.003xy - 69.985x + 0.263y + 58.740 $$ But I'm not being able to determine the ...
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1answer
16 views

Quadratic equation with greatest integer functioin

$[x]^2-7[x]+12=0$ find $x$? where $[x]$ is Greatest Integer function I have tried to solve the question like this: putting $[x]=y$ , we have the equation: $y^2-7x+12=0$ by solving this equation ...
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3answers
40 views

Nature of roots of a quadratic equation with irrational co-efficients

What would be the nature of the roots of the equation $$2x^2 - 2\sqrt{6} x + 3 = 0$$ My book says that as the discriminant is 0 so the roots are rational and equal. But discriminant can be used for ...
9
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5answers
536 views

Is $x^{\frac{1}{2}}+ 2x+3=0$ a quadratic equation

Is $$x^{\frac{1}{2}}+ 2x+3=0$$ considered a quadratic equation? Should the equation be in the form $$ax^2+bx+c=0$$ to be considered quadratic?
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3answers
47 views

Complete The Square for $x^2-10x+18$

Okay so the question is: $x^2-10x+18$ has to be written in the form $(x-a)^2+b$ and I have to provide the values of $a$ and $b$. I worked out that $a= -5$ and $b= -7$. On the video I am watching, ...
0
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1answer
42 views

IIA problem on Quadratic Equations.

How to show that expression $$\frac{px^{2}+3x-4}{p+3x-4x^2}$$ will be capable of all values when $x$ is real,provided that $p$ has any value between $1$ and $7$? Regarding my personal attempts,they ...
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2answers
67 views

Solutions for $|x^2-5x+2|=4$

Problem: Find all values of $x$ such that $|x^2-5x+2|=4$ The only way I can see to solve this would be to square both sides of the equation so as to eliminate the modulus sign. However, that ...
9
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3answers
233 views

Quadratic Equation Recurrence?

So I was playing around with the following: Let $f_0(x) = x^2 - bx + c$. If $f_n(x)$ has roots $p$ and $q$ with $p > q$, then let $f_{n+1}(x) = x^2 - px + q$. The recurrence relation is rather ...
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3answers
33 views

Finding Fall Time With Terminal Velocity

I am calculating the fall time of an object $\frac{gt^2}{2} + vt + y = \beta$ where: $g$ is -32 $v$ is 1 $y$ is 500 $\beta$ is -1000 Since I only want positive time I'll only consider the addition ...
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3answers
50 views

How do I find the value of n in the following equation [duplicate]

This is from the controversial GCSE question in the UKs recent exams. The orginal question is thus: There are $n$ sweets in a bag. $6$ of the sweets are orange, the rest are yellow. Hannah ...
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3answers
40 views

Rotate the graph of a function?

How do I rotate a graph of a function around a point, and show it in the related equation? An example could be $f(x)=\lvert x\rvert$ (absolute Value) and $f(x)=x^2$
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7answers
52 views

Square rooting to make quadratic function

If I have $x^4 - 34x^2 + 225 = 0$, is it not possible to to square root both sides of the equation so that I now have $x^2 - 34x + 15$? If this is true, then how would I go about solving the equation ...
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4answers
63 views

What two numbers when multiplied gives $-25$ and when added, $-10$?

Factors of $25$ are; $1, 5, 25$ $$5 \times 5 = 25$$ $$5 + 5 = 10$$ $$-5 \times 5 = -25$$ $$-5 + 5 = 0$$ How can I solve this? Thanks
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2answers
29 views

Emulating a parabola in my game for a jump

I am currently having some trouble understanding how to plot a parabola with the x and y coordinates.In my game a player needs to jump from point a to point b and the jump would look something like ...
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0answers
51 views

History of quadratic function

For my thesis, I have to write a short article about history and importance (applications, education) of quadratic function. Could you give some papers, books, articles about it? Thanks in advance
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1answer
83 views

How do pupils solve 2nd degree equations in Germany? (different from Spain)

I'm from Spain and in Spain the undergraduate pupils learn to solve a 2nd degree (i.e. quadratic) equation using the formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ but years ago I had a colleague who did ...
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3answers
690 views

EdExcel GCSE question about Hannah and the sweets: show that $n^2-n=90$

This is my reconstruction of the EdExcel GCSE question that has caused such a Twitter storm in the UK in the last 24 hours, along with its solution. Hannah has a bag containing $n$ sweets, 6 of ...
2
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2answers
42 views

Determinate set $A\subseteq\mathbb{R}$ so that for every $a\in A$ and every $x\in\mathbb{R}$ the condition $ax^2+x+3\ge0$ is valid

Quadratic function is always greater than $0$ if $$a>0$$ and $$D=0$$ Solving for $D$ we have $$1-12a=0\Rightarrow a=\frac{1}{12}$$ So, $$a\in[\frac{1}{12},+\infty)$$ Is this the only condition ...
2
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4answers
155 views

Show that $3$ is not a prime in $\mathbb Q[\sqrt{7}]$

Question: Show that $3$ is not a prime in $\mathbb Q [\sqrt 7] $. To show this, should I start by assuming that $3 = ab$ where $a$ and $b$ are integers in $\mathbb Q[\sqrt{7}]$ and then try to ...
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0answers
24 views

Convex quadratic problem solver gives different answers?!!

I'm not a mathematics girl but I'm pretty sure that the variance of a vector X should be a convex quadratic problem. my objective function is as follows: arg min var(sum(L) + X*L) x>0 vector X is ...
4
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3answers
54 views

Is the derivative of a quadratic related to the second difference of that quadratic?

Please do not judge me too harshly for my lack of knowledge, but at school we have gone over Quadratic functions recently. Now, these types of functions are not new to me, however when we viewed a ...
2
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3answers
42 views

Set of real $a$ so that the inequality is defined but isn't true for a real $x$

$$x(x-\sqrt {4+\log_a7})\lt \log_7 \frac a{49}$$ I reach the interval $(0,1)$ after looking for the discriminant of the quadratic to be less than zero. However, the solution in the book is an ...