The Stack Overflow podcast is back! Listen to an interview with our new CEO.

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

3,850 questions
Filter by
Sorted by
Tagged with
23 views

How do I prove that $a^2 + b^2$ is not a prime number from this given quadratic equation?

Given the quadratic equation $$x^2 + ax + b + 1 = 0$$ Where a, b are integers, and the roots are natural number. Prove that $a^2 + b^2$ is not a prime number. What should I do to prove it? Can anyone ...
21 views

Find the value of $(a, b, c)$ with $a, b, c \in \Bbb N$

$$x^2 - 2ax + b = 0$$ $$x^2 - 2bx + c = 0$$ $$x^2 - 2cx + a = 0$$ If all the roots of all three equations are a natural number, what is the value of a, b, and c?
36 views

If $\sqrt{27-10\sqrt{2}} = a+b$, where $a$ is a positive integer and $b$ is between $0$ and $1$, what is $\frac{a+b}{a-b}$?

If $\sqrt{27-10\sqrt{2}} = a+b$, where $a$ is a positive integer and $b$ is between $0$ and $1$, what is $\frac{a+b}{a-b}$? I actually have no idea how to start this question, other than to square ...
24 views

How do I express “x” from this equation?: $y=x/(x^2+1)$ [duplicate]

How do I express "x" from this equation?: $y=x/(x^2+1)$. I am not able to express it.. What I really want to do is to find out values of this function: $f(x)=x/(x^2+1)$ if the domain is R{1,-1}. I ...
64 views

For which values of $k$ does the equation $2\cos^{2}\theta +k\sin \theta + k = 2$ have real solutions?

So I take A level maths and this question was in our textbook. We solved an inequality for when the discriminant is less than zero and this gave us the same answer that is in the textbook. The ...
57 views

Is the function $f: R \to R$ defined by $y=x^{2}-2x-2$ a surjection?

The problem is to find if the following function is a surjection. $f: R\to R$ defined by $y=x^{2}-2x-2$ I know that it is not a surjection by looking at a graph of the function but I am new to ...
53 views

Find the condition for the three equations $a_rx^2+b_rx+c_r=0$; $r=1,2,3$ to have a common root.

Find the condition for the three equations $a_rx^2+b_rx+c_r=0$; $r=1,2,3$ to have a common root. My attempt is as follows: \begin{equation} a_1x^2+b_1x+c_1=0\tag{1} \end{equation} \begin{equation} ...
36 views

25 views

parallel shortest distance between graph of parabola and line [on hold]

I would be really thankful if someone could explain how I can approach this problem. (Not only this one but this type of finding the distance between parabola and line) Problem n32 ECONOMICS ...
36 views

60 views

Find $a\in \mathbb{R}$ for which $a\cdot \left(\frac{1}{1+x^2}\right)^2-3\cdot\frac{a}{1+x^2}+1=0$ will have all roots imaginary

Find $a\in \mathbb{R}$ for which $a\cdot \left(\frac{1}{1+x^2}\right)^2-3\cdot\frac{a}{1+x^2}+1=0$ will have all roots imaginary. My attempt is as follows:- Let $t=\frac{1}{1+x^2}$, and let's find ...
30 views

Graph of $x^2$ + $y$ $=$ $0$ is an upward or a downward opening parabola?

That is my exact question. If we graph $x^2$ + $y$ $=$ $0$, do we get a downward opening parabola? Let me explain what actually got me confused. I know that $y$ = $x^2$ is an upward opening parabola ...
35 views

Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has

Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has 1) exactly two distinct negative roots 2) at least two distinct negative roots I tried to factorize it but ...
44 views

Solve for k, $f(x)=x^2+2(k-1)x+k+5, k\in R$

If the graph of the function $f(x)=x^2+2(k-1)x+k+5, k\in R$ cut the x-axis at least at one point on the positive side , find the set of possible values of the constant k. My attempt is as follows: ...
20 views

Finding a direct function for $f_n = f_{n-1} + (x-a_{n-1})^2$ where $a_{n-1}$ is root of $f_{n-1}$ closest to $\alpha$ and $f_1 = x-a$.

Problem Suppose $f_1 = (x-a)$ and $f_n = f_{n-1} + (x-a_{n-1})^2$ where $a_{n-1}$ is a root of $f_{n-1}$ closest to $0$. Is there a function for $f_n$ that only depends on $x$? Examples As a first ...
49 views

How to prove that $B = A^{-1}$ ? If A and B are 2 x 2 matrices where $B \neq I_2$ such that $( A + B )^2 = A^2 + 2AB + B^2$

If $A \text{ and } B \text{ are } 2\times 2$ matrices where $B\neq I_2$, such that $(A+B)^2 = A^2 +2AB + B^2$, deduce that $B = A^{-1}$ If $A = \begin{bmatrix}1&2\\9&-1\end{bmatrix}$ ...