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

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quadratic equation question

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. the distance travelled before it reached the ground is as follows... s = Uot + 1/5gt2 where Uo ...
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5answers
47 views

Solving a quadratic trigonometric equation?

The equation is $6 \cos^2x+\cos x=1$, My work: $6x^2+x-1=0$ $(3x-1)(2x+1)$ $3x-1=0 ∨ 2x+1=0$ $x=\frac{1}{3} ∨ x= \frac{-1}{2}$ But I do not know how to progress further.
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0answers
22 views

A question using quadratic equations.

A ball is thrown down at 72km h-1 speed from the top of a building. The building is 125 metres tall. the distance travelled before it reached the ground is as follows... s = Uot + 1/5gt2 where Uo ...
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3answers
41 views

Using sum/product of quadratic roots to solve cubic equation

Given $\alpha$ and $\beta$ are the roots of the quadratic equation $6x^2 + 2x - 3 = 0$, how do I find the value of: $$ \alpha^3 + \beta^3 $$ and: $$ \frac{1}{\alpha^3} + \frac{1}{\beta^3} $$ ...
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1answer
26 views

Quadratic equation solutions [closed]

Quadratic equations, which are expressed in the form of $ax^2 + bx + c = 0$, where $a \ne 0 $ does not equal 0, may have how many solutions? Explain why.
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5answers
75 views

Distribution of integer solution pairs (x,y) for $2x^2 = y^2 + y$

I am looking for integer pairs $(x,y)$ that respect $$2x^2 = y^2 + y$$ For example $(6,8)$ is a solution for that. Simple solution is to enumerate on $x$ or $y$ and test if the corresponding ...
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1answer
31 views

Find domain of function with quadratic numerator algebraically

I'm stuck on this problem: $$f(x) = \frac{x^2 -4}{x}$$ I need to determine why this function's domain is not: $$\{x|x \neq \pm 2\}$$ All of the examples that I've seen have the quadratic in the ...
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2answers
31 views

How to prove one of these equations has real roots?

Question: If $\;a,\, b,\, c,\, d \;$ are real and $\;ac = 2( b + d) $ ,then show that at least one of the equations: $\; x^2 + ax + b = 0 \;$ and $\; x^2 + cx + d = 0 \;$ has real roots. I've ...
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3answers
35 views

Quadratics with unknowns

If $5x^2 – t = 4x$, and $x$ and $t$ are both positive real numbers. What is $x$ equal to? How do you find $x$? Is there a specific formula?
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2answers
57 views

Finding the probability an equation has real roots.

If $Q$~UNIF$(0,3)$, find the probability that the roots of the equation $g(t)=0$ are real, where $g(t)=4t^2+4Qt+Q+2$. There was a similar question asked that I looked at, but I am still a little ...
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1answer
19 views

Quadratic factor to complex numbers

How to convert this quadratic factor to complex number form? (With steps please) Reference: $Z = a + bi$, $i = \sqrt{-1}$ $$-3 + \frac{\sqrt{-12}}{2}$$ Thanks!
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0answers
16 views

system of two quadratic equations with two variables

Is there a general way to solve exactly a system of this shape (the $a_i$ are constants): $$\begin{array}{cc}a_1x^2+a_2x+a_3y^2+a_4y+a_5=0\\ a_6xy+a_7x+a_8y+a_9=0 \end{array} $$ It comes from a ...
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1answer
97 views

When is $(x+3)^2$ equal to $x^2 +9$?

http://matheducators.stackexchange.com/a/1400/775 Someone commented that the equation in the above answer might sometimes be correct after I commented a correction (feel free to rewrite it ...
2
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1answer
51 views

Nonlinear first order ODE with quadratic in the derivative

This equation shouldn't be so hard, and yet I'm stymied. $$ \left( \frac{dw}{dz} \right )^2 + \alpha \frac{dw}{dz} + w \beta = 0 $$ with $w(0) = w_0>0$ $w(L) = 0$ for some known L and ...
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1answer
51 views

Type of this Conic section

I want to determine, to which type the following Conic sections belong to: $$ \begin{align} \textrm{(i)}&\quad-8x^2+12xy-6x+8y^2-18y+8=0\\ \textrm{(ii)}&\quad5x^2-8xy+2x+5y^2+2y+1=0 ...
0
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1answer
25 views

Find roots of binomial expression by replacing some variables?

So we have the binomial expression * I might be not using the correct term,english isnt my first language* $$ \left[1- \frac 34e^{-j2\pi\cdot f} + \frac 18e^{-j4\pi \cdot f} \right]$$ How do I find ...
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4answers
39 views

Finding the three unknowns

Can someone show me the steps to finding the three unknowns of these two equations. $$-a-bx+cx^2 = x^2+2x+1$$ The answers are $a=\ ...\ $, $b=\ ...\ $, and $c=\ ...$ , but I can't see how they ...
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1answer
43 views

Homework: canonical form of quadratic form

X=(x,y,z) Q(X) = $x^2 + 4xy + 6xz + 3y^2 +8yz +5z^2 $ I got by using completing the square method: Q(X) = $(x+2y+3z)^2 - (y+2z)^2$ so as I learned now I do: $u = x+2y+3z$ $v = y+2z$ $w = 0 $ ...
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1answer
17 views

system of equations solving with only that information

Hi would would I go around to solve the following, there is no other information stat is given other than the fact that i have already expanded this from this $(25-y)(x+8)=523$ $25x-8y=323$
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1answer
40 views

Calculate the volume of water in glass over time.

For A) I found that volume should be defined by But I got no idea what to do in b) and c)
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0answers
49 views

Showing DO NOT exist GCD of $6$ and $2+2 \sqrt{-5}$ in $\Bbb Z[\sqrt{-5}]$.

Showing DO NOT exist gcd of $6$ and $2+2 \sqrt{-5}$ in $\Bbb Z[\sqrt{-5}]$. I tried it. Suppose $d$ is GCD of $6$ and $2+2 \sqrt(-5)$. then there exist $x,y \in \Bbb ...
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0answers
10 views

Finding absolute position on a Bezier Curve with constant speed

i work on a graphic project using bezier curves. I have an equation P(t), representing a cubic Bezier, with control points A, B, C, D. This equation is as follow: $$ ...
2
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1answer
61 views

Expanding Square Roots, Why No Negative?

I haven't thought through algebra in a while and the last explanation I received of this seemed arbitrary. I hope I can get some clarification here. I understand that $\sqrt{+a} = \pm b$. Here's ...
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0answers
35 views

Quadratic inequality with parameter

Hi I've got this inequality with parameter $a\in R$ $\frac{x+a}{x}\le x+2$ I've solved it but I've got different results than book. I've done it by dividing it into 2 cases. 1. x<0 2. x>0 and then ...
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7answers
86 views

How to find $x^2 - x$?

I'm quite a novice when it comes to maths. I'm on a problem in which I have had to isolate $x$ , through factorials which I completed without problem. However, now I am stuck on a seemingly more minor ...
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1answer
26 views

Proof of axis of symmetry [duplicate]

How do you prove -b/2a the Axis of symmetry equation using the Quadratic formula?
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2answers
37 views

Proof of axis of symmetry equation [closed]

Because quadratic functions are symmetrical how do you prove the axis of symmetry equation. $x=(-b/(2a))$
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1answer
71 views

Find pressure in a sinusoidal function

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with laughing gas. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 ...
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2answers
36 views

What are the parameters of a parabola

In the following figure I understand the $bx+c$ part. It is simply the equation of a line. But I don't understand where did $ax^2$ came from? What exactly is it? What does $a$ tell us about a ...
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2answers
41 views

Find maximum of a system of equations

You have 300 meters of fencing with which to build two enclosures. One will be a square, and the other will be a rectangle where the length of the base is exactly twice the length of the height. (a) ...
6
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3answers
88 views

Solve $x^{3}-3x=\sqrt{x+2}$

Solve for real $x$ $$x^{3}-3x=\sqrt{x+2}$$ By inspection, $x=2$ is a root of this equation. So, I squared both sides and divided the six degree polynomial obtained by $x-2$. Then I got a ...
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5answers
47 views

How do you factor a quadratic expression, without using the formula?

I am asked to factor $2x^2 -3x+1=0 $ using factorization, but I run into fractions, and it becomes very messy and complicated to deal with, especially since specifically asked not to use the formula. ...
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4answers
133 views

How can I solve equation $x^2 - y^2 -2xy - x + y = 0$?

I have this equation with 2 variables - $$x^2 - y^2 -2xy - x + y = 0$$ The only condition I have is that $x + y$ should be greater than $10^{12}$. EDIT - I need $x$ and $y$ to be integer. I ...
3
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3answers
201 views

Algebraic Relationships - Quadratic Equations

I am having a tough time with the following question: If $x$ is real and $p=3(x^2 + 1)/(2x-1)$, then prove that $p^2 - 3(p+1)\geq 0$. I don't know how to tackle this question. Thanks for your ...
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4answers
33 views

Completing the square with second degree coefficient greater than one

How do I complete the square when the second degree coefficient is greater than one. I can do it when $x^2+4x-4=0$, for example, but I can't work out how to do when $3x^2+4x-4=0$.
6
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3answers
111 views

How to solve the following? $ x^3+1=2{(2x-1)}^{1/3} $.

Find all the real solutions of $$x^3+1=2{(2x-1)}^{1/3} $$ I tried to cube both sides but got messed up with a nine degree equation! Please help. Thanks in advance!
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4answers
39 views

Quadratic equations and probability

The inequality: 4p^2-17p+4>0 Solving using quadratic equation: (−(−17)±√(−17)^2−4⋅4⋅4)/8 =(12±√225)/8 I realize why p = 4 or p = 1/4, and in this case p represents and probability so the solution ...
3
votes
2answers
67 views

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$, then prove that $P(x) \cdot Q(x) = 0$ has at least two real roots?

How should i solve the same? I assumed the roots be $ \alpha, \beta $ for $ P(x) $ and $ \gamma, \delta $ for $ Q(x) $. Product of roots turn out to be of the opposite signs, being $$ \alpha \cdot ...
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1answer
24 views

Find values of the parameter a so that equation has equal roots.

$x^2+2a\sqrt{a^2-3}x+4=0$ My final result was 2 and -0.5. Was it correct?
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1answer
39 views

Quadratic equation problem. Composition of functions

Suppose $p(x)$ and $q(x)$ are quadratic polynomials and the three largest roots of $p(q(x))$ are $10$, $20$ and $23$. What is the smallest root of $p(q(x))$? Then, there will be 4 roots. $q(10)$ ...
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1answer
30 views

Request for help with a quadratic polynomial question.

If the rooots of the equation $x^2+bx+c=0$ are real , show that the roots of the equation $x^2 +bx+c(x+a)(2x+b)$ are again real for every real number a. I assumed the discriminant of the first ...
2
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2answers
30 views

Fitting a quadratic polynomial to two points such that it is always concave downward

Given two points $(x_1, y_1)$ and $(x_2, y_2)$, I'd like to construct a quadratic polynomial of the form $y = a_2x^2 + a_1x + a_0$ such that it intersects both points and is concave downward (i.e., ...
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3answers
23 views

How to invert these equations

Apologies in advance as maths has never been my strong point (I'm not even sure which tag to use). I'm developing some software that uses some equations to convert values being read from a hardware ...
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1answer
74 views

Isolate “a” in a quadratic function

You have a quadratic function: $ax^2 + bx + c = y$. If you know $b$ and $c$, are able to plug any domain value $x$ into this blackbox equation and receive a range value $y$, and do not know the vertex ...
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2answers
95 views

Where did Harry go wrong solving his equation? [closed]

Harry is trying to solve the equation $y = 2x^2−x−6$ using the quadratic formula. He has made an error in one of the steps below. Find the step where Harry went wrong. In which step did he go wrong? ...
0
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0answers
9 views

Quadratic function as permutation of sequence

Say I have a $n \in \mathbb{N}$ and $$a_i := (1,2,...,2^n)$$ and two function $$f(i) = \sum_1^i i = \frac{i(i+1)}{2}$$ $$g(i) = f(i) mod 2^n$$ When I now look at a new sequence $$b_i = (a_{g(0)}, ...
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1answer
21 views

How to find quadratic function in vertex form from two points?

I'm starting to learn about quadratic formulas in math class. This question came up in a homework packet: A WNBA player takes a three-point shot 22 feet away from the basket, The ball reaches ...
2
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2answers
45 views

Solving a fractional quadratic equation problem by completing the square

I have the following problem to solve using the method of completing the square. $$2x^2-3x-1 = 0$$ Here is where I've gotten to so far on this problem. $$2x^2-3x = 1$$ $$x^2-\frac{3}{2}x = ...
1
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1answer
44 views

how should i go about solving the following problem??

$f(n)=a^n-b^n$ where $a$ and $b$ are roots of the following equation .$$5x^2-2x+1=0$$ Then find the value of $$\frac{5f(10)+f(9)}{f(8)}$$ I realised we can use the 5 in the equation as $\frac{1}{ab}$ ...
0
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2answers
35 views

Prove that $g(x) > 0$

If $f(x)$ is a quadratic expression such that $f(x) > 0,\ x\in\mathbb{R}$ and if $g(x)= f(x) + f'(x) + f''(x)$, then prove that $g(x) > 0, \ x\in\mathbb{R}$.