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

learn more… | top users | synonyms

2
votes
4answers
41 views

What does 'express in terms of $x$' mean?

For the following question : $f(x) = 2x^2 + 4x $ It asks me to express the following in terms of $x$: $f(-2x)$ What does the question mean by this? Does it mean make $x$ the subject?
9
votes
0answers
22 views

Intersection of two hyperplanes

$G$ and $H$ are hyperplanes in $\mathbb{P}_n$ with coordinates $g=(g_0, \ldots, g_n)$, $h=(h_0, \ldots, h_n)$. How can I find a symmetric matrix $A_Q$ of a quadric $Q$ with $ Q = G \cap H$, where ...
1
vote
1answer
18 views

max and minimum qudratic function problem

A piece of wire $20$ metres long is cut into $2$ pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum. ...
13
votes
0answers
144 views
+50

An interesting table of Prime Generating polynomials similar to $n^2+n+41$?

Here is some data on quadratic prime generating polynomials of a particular form. Kindly look at the questions given below it. $$\begin{array}{cccc} \text{#} & P(n)=an^2+bn+c\,; & d = ...
0
votes
2answers
33 views

Factorize this polynomial $ax^2+bx+c$ into factors of the first exponent in the cases when D>0, D=0

The previous request was to prove the identity $ax^2+bx+c=a[(x+(b/2a)^2-(D/4a^2)]$, where $D=b^2-4ac$ And I proved it from the left to the right, which means I managed to express $ax^2+bx+c$ as ...
0
votes
1answer
14 views

Finding the y-vertex of a function and X2.

I am trying to solve the following exercise: The graph of the fuction $y=-2x^2+bx+c$ passes through the point (1,0) and has as its vertex the point (3,S). What is the value of s? Options: A -5_____ ...
0
votes
1answer
34 views

Discriminant of Quadratic with circle

The circle $x^2 + (y - c)^2 = r^2$, where $c > 0$ and $r > 0$, lies inside the parabola $y = x^2$. The circle touches the parabola at exactly two points located symmetrically on opposite sides ...
-2
votes
2answers
45 views

probability of winning a game between harsha and ramya [closed]

Harsha is going to pick three non-zero real numbers, say, a, b and c and Ramya is going to arrange the three numbers as the coefficient of a quadratic equation ax2 + bx + c = 0. Harsha wins the game ...
0
votes
0answers
15 views

Making equations for parabolas

When using the equation $y=a(x-s)(x-t)$ you are given the zeros of the quadratic are $0$ and $6$ and the minimum value is $-9$. What does the equation of the parabola look like?
0
votes
1answer
20 views

What can the “Product of Roots” be used for in quadratic form?

If I have a linear function and some kind of quadratic in x and y ie: $x^2+xy+y^2=1$ that share two roots, then I can substitute that linear function into the quadratic expression and use the Sum of ...
0
votes
1answer
16 views

Grade 10 Quadratic equation

This was on my year 10 maths test and I gave up with 40 mins to complete: Basically you were given the coordinates: y intercept : (0,10) 1 x intercept: (10,0) and y value of the vertex: +15 Can ...
0
votes
1answer
16 views

Writing a equation in vertex form with an axis of symmetry, maximum height, and a point that it crosses

Suppose a parabola has an axis of symmetry of $x = -7$, a maximum height of $4$, and passes through point $(-6, 0)$. Write the equation in vertex form. Here's what I got: $y = -(x + 7)^2 + 4$ The ...
1
vote
1answer
34 views

Polynomial function question

If $f(x)$ is equal to $\frac{1}{x^3 + 3x^2 + x}$, find the smallest value of $n$ for which $f(1) + f(2) + ... F(n) = \frac{503}{2014}$. I tried noting that first initial values of f sum to ...
1
vote
1answer
26 views

Determine all values of n such that this quadratic

Determine all values of $n^2 + 19n + 99$ is a perfect square. I tried setting some square $b^2$ equal to the following, and then factoring as a Diophantine equation with $2$ variables... Didn't work.
0
votes
4answers
53 views

Quadratic equation $3x^2 + x - 2 = 0$

I have $3x^2 + x - 2 = 0$ and the answers are supposed to be $-1$ and $2/3$. It was in the quadratic formula chapter so I tried to use that but since the middle x is only 1 for a coefficient, it ends ...
0
votes
2answers
45 views

Quadratic programming for special equation issues

My problem is how to find $\tau_1$ and $\tau_2$ s.t maximize the objective function is $$E=M-\alpha V$$ subject to $$-0.0062\le\tau_1\le0.499$$ $$-0.479\le\tau_2\le0.0262$$ $$\tau_1+\tau_2\le0.02$$ ...
1
vote
5answers
149 views

completing the square to solve equation

Is it possible to use the method of completing the square to solve the equation $2x^2+18x+21=0$ ? I have problem with how to remove the negative sign on the right side.
0
votes
2answers
29 views

Quadratic expression into postfix notation

I know generally how to convert an infix expression into a postfix expression; but I came lately across this quadratic expression: $\left(4y^2 + 2x - 1\right)$ that I had to convert into postfix and ...
2
votes
4answers
37 views

Solve $\frac{1}{2}kx^{2}-cx=\frac{1}{2}ky^{2}+cy$ for $y$

I have the equation: $\frac{1}{2}kx^{2}-cx=\frac{1}{2}ky^{2}+cy$, where $k$ and $c$ are arbitrary constants. How do I go about simplifying this and solving for $y$ in terms of $x$, excluding the ...
2
votes
1answer
21 views

For $f(x) = ax^2 + bx +c$, why is it written $a(x-h)^2 + k$

I'm going to have to teach how to graph quadratic equations. Since we've already done a lot of work with the Quadratic Formula, the students are more or less familiar with the standard notation of a ...
2
votes
3answers
20 views

Conceptual problem in solving quadratic equation

The sum of all real roots of the equation $$|x-2|^2 + |x-2| - 2 = 0$$ is? I tried this problem by taking two cases $x<2$ and $x>2$ and solving the corresponding equations and I got $8$ as the ...
0
votes
1answer
74 views

Can a quadratic be solved with matrices?

The question, pure curiosity, is whether you can solve a quadratic with the use of matrices? And if yes, does that method also work for higher polynomials? Say for example I have a quadratic such as ...
0
votes
1answer
34 views

If $\alpha,\beta$ be the roots of $ax^2+bx+c=0 (a,b,c \in R)$

If $\alpha,\beta$ be the roots of $ax^2+bx+c=0 (a,b,c \in R) , \frac{c}{a}<1$ and $b^2-4ac <0$, $$f(n) \sum^n_{r=1} (|\alpha|^r +|\beta|^r)$$ then $$\lim_{n\to \infty} f(n) $$ is equal to ? Sum ...
0
votes
1answer
22 views

Find the domain and range of a quadratic [duplicate]

$$F(x)=\frac {x^2+ax+1}{x^2+x+1}$$ Find the complete set of values of 'a' such that $F(x)$ is onto And f(x) maps from real numbers to real numbers.
0
votes
0answers
25 views

Finding the domain and range of a function

$$F(x)=\frac {x^2+ax+1}{x^2+x+1}$$ Find the complete set of values of 'a' such that $F(x)$ is onto And f(x) maps from real numbers to real numbers.
1
vote
1answer
43 views

quadratic equation

A garden is in the shape of a rectangle, $20$m by $8$m. Around the outside is a border of uniform width and in the middle is a square pond. The area which is not occupied by either border or pond is ...
1
vote
4answers
43 views

quadratic equation: $5x^2 + 9x - 170 = 0$

I have a problem, my textbook says the solution of $5x^2 + 9x - 170 = 0$ is $5$ but the book didn't describe how it solved the equation. How can I solve this?
0
votes
0answers
31 views

Trouble simplfying quadratic indentity

I'm struggling to follow the derivation below: $u_j=\frac{\sigma^4+ \theta^2\delta_j^2\alpha_j^2+2\theta\sigma^2\delta_j\alpha_j}{\sigma^2+\delta_j^2\alpha_j^2} \leq \frac{\sigma^4+ ...
1
vote
0answers
41 views

Solving matrix equation of the form $(AX)^2+(BY)^2=D$

Is there any method that can solve the matrix equation of the form $(AX)^2+(BY)^2=D$? $A$ and $B$ are matrices, $X$, $Y$ and $D$ are column vectors. (Solve for $X$ and $Y$) I originally have two ...
5
votes
2answers
451 views

How to solve this equation? Can I treat as a quadratic equation?

$$\ln(x+3)+\ln(x-4)=0$$ How to solve this equation? First removing the 'ln' from the equation and after making a quadratic equation and then solve the quadratic equation?
0
votes
1answer
33 views

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$

If the roots of $x^2+x-1$ are $\alpha$ and $\beta$, find an $eq^{n}$ whose roots are $\alpha^{19}$ and $\beta^{7}$ My Procedure The roots are $$\frac{-b+\sqrt{b^{2}-4ac}}{2a}$$ and ...
-2
votes
1answer
39 views

List the elements of the set $\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$ [closed]

I don't get this maths equation Can anybody explain it ? Thanks List the elements of the following set: $A=\{X \in \mathbb Z \mid 4X^2 +11X = 0\}$.
1
vote
1answer
19 views

Evaluating cubic roots of a quadratic

If $\alpha$ and $\beta$ are the roots of the quadratic equation $2x^2 + 4x -5 = 0$, evaluate $\alpha^3 + \beta^3$.. I know that $$\alpha + \beta = \frac{-b}{a}$$ and $$\alpha \beta = ...
1
vote
2answers
28 views

Factor the Quadratic

-16t^2+32t+20=0. How are you supposed to find -5 and positive 1 to put in the parenthesis? -4(2t-5)(2t+1)?
-1
votes
3answers
48 views

Inequalities - x^2 - 1/2 x - 5 < 0 ; why is x > 2 1/2?

Question : $$\text{ find the set of values of }x \text{ for which } $$ $$10 + x - 2x^2 < 0$$ Answer : $$x < -2$$ $$x > 2\frac{1}{2}$$ EDIT - thanks for the responses. To try and ...
2
votes
1answer
94 views

Quadratic Irrationality of the Periodic points of the Gauss map

If $G:[0,1] \rightarrow [0,1]$ is the Gauss map which is defined as $$G(x) = \left\{\frac{1}{x}\right\} = \frac{1}{x} - \left\lfloor\frac{1}{x}\right\rfloor,$$ show that if $x$ is periodic of order ...
0
votes
1answer
47 views

Issue on proving quadratic formula

I have come across a stage of the proof: $$ \left(x+\frac b{2a}\right)^2=\frac{b^2-4ac}{4a^2}$$ How does $\left(x+\frac b{2a}\right)^2$ not equal $\pm x\pm \frac b{2a}$ when taking the square root?
0
votes
1answer
21 views

Inequalities and equations - creating sets from quadratic equations.

My question is just making sure that my working is correct and that I understand properly (self teaching, can get confused...) So question : Find the set of values for which $$x^2 -4x-12 < 0$$ ...
1
vote
3answers
66 views

Factorize $6x^2 -5x -14 = 0$

I'm throwing a bit of a blank on the best way to factor this : $$6x^2 -5x -14 = 0$$ I know that I could multiply $6$ by $14$ and then find a pair of factors that add to $-5$ (b), but this feels a ...
0
votes
1answer
55 views

intersection of 4 circles

Hi I'm doing some programming challenges for fun and I am trying to work out the maths required to solve this problem. It has been 10 years since I did any maths in anger like this so i'm a bit ...
0
votes
2answers
19 views

Help with demonstration of formula for the axis of a parabola

At school we are studying the parabola and our teacher said that the formula for the axis of a parabola is $x=-\frac{b}{2a}$ without giving us the demonstration; so I tried to come up with a nice ...
0
votes
0answers
13 views

Changing Variables Method for Solving a Quadratic Equation

I am reading a book that contains different ways of deriving the quadratic equation. One of the methods that it discusses is "Changing the Variables." It contains an exercise that I don't understand: ...
0
votes
1answer
32 views

Quadratic $y = -4.9x^2 + 25x$

Here is my questions, please help. In the game of foot, a team can score by kicking the ball over a bar and between two uprights. For a kick in a particular game, the height of the ball above the ...
0
votes
2answers
26 views

Prove the given condition from given two quadratic equation

Question: If the quadratic equations $x^2+bx+c=0$ and $bx^2+cx+1=0$ have a common root then prove that either $b + c + 1 = 0$ or $b^2 + c^2 + 1 =bc + b + c$ Till yet, I had figured the common ...
1
vote
1answer
25 views

Checking some work on finding roots

OK, I have the following response function: $$H(\omega) = \frac{1-\omega^2 LC}{1+\omega^2 LC - i \omega RC}$$ I want to find where it becomes $\frac{1}{\sqrt{2}}$. This should be simple enough. ...
0
votes
1answer
36 views

Simplification of another nasty expression

I have the following condition $$ 2 \frac{x^2}{y^2} \left(1 - \frac{1}{y^2} \right)+ \frac{1}{y^2} \leq 1$$ Can anyone help me simplify it to the best possible relationship between $x$ and $y$?
0
votes
1answer
18 views

Find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$

I'm trying to find the range of values $k$ can take given that, for real $x$, $f(x) = \frac{x^2+3k}{x+k}$ can take any real value. These are the steps I've taken so far: $$ xy + ky - x^2 - 3x = 0 $$ ...
0
votes
2answers
20 views

Find the range of $k$ in $f(x) = \frac{x^2-k}{x-2}$

I have the following question: For real $x$, $f(x) = \frac{x^2-k}{x-2}$ can take any real value. Find the range of values $k$ can take. Here is how I commenced: $$ y(x-2) = x^2-k \\ -x^2 + xy - ...
-1
votes
1answer
68 views

If the quadratic equation $x^2 + 2kx + 2(k + 4) = 0$ has distinct real roots, then $k^2 – 2k – 8 > 0$ [closed]

The quadratic equation $x^2 + 2kx + 2(k + 4) = 0$ has distinct real roots. Show that $k^2 – 2k – 8 > 0$. I'm not sure what you're meant to do here- it's a 2 mark question.
3
votes
1answer
60 views

Why doesn't this method of solution work?

Solve $$\sqrt{2x^2 - 7x + 1} - \sqrt{2x^2 - 9x + 4} = 1 \tag1$$ I tried to do the following: $$(2x^2 - 7x + 1) - (2x^2 - 9x + 4) = 2x-3\tag2$$ Dividing $(2)$ by $(1)$ yields $$\sqrt{2x^2 ...