Mathematics Stack Exchange
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Questions tagged [quadratics]

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 $y=a(x+b)(x+c)$.

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 $y=a(x+b)(x+c)$.

The root of $y=ax^2+bx+c$ can be solved by the formula $$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

5400 questions
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Quadratic equation with roots

The quadratic equation $2x^2 + 7x + 5 = 0$ has a roots $α$ and $β$. Form a quadratic equation with roots $3α$ and $3β$.
Eppy Eka
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theory of equation..finding roots of a modular function

The number of real roots of $\big|x^2+4|x|+3\big| +2x-11=0$ is? I have tried by expanding modulus, and if I'm right I'm getting two real roots but I'm a bit confused because of the innermost modulus, please help
Nitin Jha
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How to solve quadratic equation problem having a prepositional logic?

When $\alpha,\beta$ are roots of $x^2+bx+c=0$, Find the equation whose roots are $p$ and $q$ where, $p=\alpha +\beta^2,\,q=\beta+\alpha^2$. Also when $\alpha,\beta$ are imaginary show that, $b=-1\,$if and only if $p,q$ are real. So far I have…
emil
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Applying quadratic equations.

So I realise this is quite an easy question, but for some reason I can't see the solution. So the question followed on from a previous question where we used a quadratic equation to find the dimensions of a right angle triangle. This question is:…
MEcho
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In this proof ( simplified version of Vieta's Theorem), do they use intercept form to prove it or am I just confused?

Picture of proof I was thinking that someone could give me some insight on this proof in general.
Ozymandias
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Which integers fit $1=\dfrac{2}{x^2}+\dfrac{3}{y^2}+\dfrac{4}{z^2}$

I am having trouble with the following question: For which integers $x$, $y$ and $z$ is the following statement correct? $$1=\dfrac{2}{x^2}+\dfrac{3}{y^2}+\dfrac{4}{z^2}$$. Obviously, $x=3$, $y=3$ and $z=3$ is one answer. How do I prove that it is…
Dreuhn
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Proving $x-8$ is equal to $x^{2}- 64$

Okay so I have this trick question that I can't seem to figure out. Suppose $x = 8$ and $x^2 = 64$, then $x -8 = 0$ and $ x^2- 64 = 0 $. Now comparing both since they are equal to zero, $x - 8 = x^2 - 64 \Rightarrow x - 8 = (x+8) (x-8) \Rightarrow…
Ramsha Khalid
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Stuck on this problem based on theory of equations/Quadratic equations

I need help with this question. I'm stuck on it. I'll show how I approached this question, but I couldn't get very far. $P(x) = x$ has no real roots => $P(x) - x$ has no real roots => $ax^2 - (b-1)x + c$ has no real roots =>$ P(x) - x \gt…
4d_
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Possible values of a variable in a quadratic equation

Find all values of $a$ for which the equation $2x^2 - 2(2a + 1)x + a(a-1)=0$ has roots $\alpha$ and $\beta$ satisfying the condition $\alpha \lt a \lt \beta$. My attempt : I have observed the coefficient of $x^2$ here is $2 \gt 0$. I tried to…
MathsLearner
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How to find range of a Quadratic/Quadratic function easily without plotting its graph?

Is there any way to find range of a Quadratic/Quadratic function, without plotting its graph?
Sheb
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Find the value of $\frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+b}$+$\frac{\beta^2+2\beta+1}{\beta^2+2\beta+b}$

If $\alpha$ and $\beta$ are the roots of the equation $x^2-a(x+1)-b=0$ Find the value of $\frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+b}$+$\frac{\beta^2+2\beta+1}{\beta^2+2\beta+b}$ I tried to multiply by $\beta^2$ to first fractional part but…
Samar Imam Zaidi
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How to prioritize signs

Make n the subject of the formula: $$ P=400n^2-1280 $$ Why is the answer $$ n= \sqrt\frac{P+1280}{400} $$ And not $$ n=\sqrt{\frac{P}{400}+1280} $$
IZZLIEDAT
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If $\alpha $ is a root for $ x^2-2x+3=0 \implies \alpha^2-2\alpha^3=9 $

If $\alpha $ is a root for $ x^2-2x+3=0 $, Proove that $\alpha^2-2\alpha^3=9 $ I have tried the following, since $\alpha$ is a root, it should satisfy the equation. Hence, $$\alpha^2-2\alpha+3=0 $$ Since this equation has complex roots, other…
emil
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Solve equation: $\sqrt{x^2+x+1}=1-x-x^2$

$$\sqrt{x^2+x+1}=1-x-x^2$$ I am doing this problem for about an hour and I cant get to all the results. What is the easiest way to do this? I tried by squaring everything right away but at the I end I get a pretty messed up equation that is not easy…
RiktasMath
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Find sum of $a+b+c+d$

If $x^2-10ax-11b=0$ have roots $c$ and $d$. $x^2 -10cx-11d=0$ have roots $a$ and $b$ then the value of $a+b+c+d$ is.. Here from both equations, $c+d =10a$ and $a+b = 10c $ and $ac =121$. But how I can get the sum $a+b+c+d$ from these! Please help.…
Hritik
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