Mathematics Stack Exchange
Mathematics Stack Exchange

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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Roots of Quadratic Equation and its nature?

For what value of k will 3x^2 + 5x + k = 0 have Equal roots? For Equal roots discriminant should be equal to zero. So what would be the value of k?
zonnie
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Quadratic equations question

let $P(x)$ and $Q(x)$ be 2 quadratic eqs. with one non-rational root common and integral coefficients. prove $P(x) = r.Q(x)$, for some rational no. $r$ TRIED ANSWER: Let $P(x)= ax^2 + bx + c$ $\Rightarrow$ $x = \frac{-b \pm \surd b^2-4ac}{2a}$ Let…
Alok Ranjan
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Quadratic Equations and graphs

A bridge forms a parabolic arch. The span of the arch is 80 meters and its centre is 15 meters above either end. Write a quadratic equation that models the arch.
Steve dumonski
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Confusion with qudratic equations

According to my book In the given equation $$x^2+x+1=0\tag{1}$$ If $a$ is a root of eqn $(1)$ then $a$ satisfies the following equation $$a^2+a+1=0\tag{2}$$ $$\implies (a-1)(a^2+a+1)=0\tag{3}$$ $$a^3=1$$ How do you get the last $3$ equations?…
Ghost
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How to find possible equations given 2 points and the $y$-value of a vertex

If I have 2 points (let’s say $(0,8)$ and $(6,0)$) and a line on which a vertex can be ($f(x)=16$), how can I find the possible quadratic equations that would intersect both the points and have the vertex lay on that line?
TheOneAndOnly
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A condition for the roots of a quadratic equation

If $x=p$ lies within the roots of the quadratic equation $f(x)=Ax^2+Bx+C=0$ then we demand $(i):B^2>4AC$ and $(ii):Af(p)<0$. I want to know if the condition (i) is superfluous here. Or whether the condition $(ii)$ would alone be sufficient here.
MathDona
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If $x^2 + mx + 1 = 0$ and $x^2 + x + m = 0$ share a same root ($m \neq 1$), find $m$

I'm certain there must be a certain formula/theorem involved but I haven't learnt about it. Rather than simply being given the answer, could I be given short and concise useful tips for questions like these in the future? Much thanks in advance.
Rae
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Where can we take square root both the sides and where we can't?

Recently I have been solving a electrostatics questions where you are given two charges and want to find where the third charge should be kept so that net force on it is 0. It generates a quadratic equations which can be solved and correct answer…
swarnim
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Why do some quadratic graphs have a flat bottom?

Why do some quadratic graphs have a flat bottom? This is concerning sketching the graph on a physical graph. An example of it would be the equation:y=x^2 -5x+4
user324713
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Two Quadratic Equation having real roots

Let $x^2 + 2ax + b = 0$ and $x^2 + 2bx + a = 0$ have real roots $(a,b > 0)$, then minimum possible integral value of ab is___________ My approach is as follow $T(x)=x^2 + 2ax + b = 0$, hence $4a^2-4b\ge 0$ $U(x)=x^2 + 2bx + a = 0$, hence $4b^2-4a\ge…
Samar Imam Zaidi
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Prove the following for the given quadratic

If the difference of the roots of $x^2-px+q=0$ is unity then prove that $p^2-4q=1$ and $p^2 =4 q^2=({1+2q})^2$ What I Tried 1.I proved the first part of the question using the understanding of the difference of the roots $$D^{1/2}/|a|=|a-b|$$ for …
Rishav Bhagat
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Is there a method to factor equations with two variables raised to the second power?

I found the equation $2b^2-ab-a^2=0$ on a problem and couldn't find a way to factor it. Is there any method to factor these types of equations?
ラゴズ
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Solving $x^5 - 2x^3y^2 + xy^4 = y^2$

Find all integer solutions to the equation $$x^5 - 2x^3y^2 + xy^4 = y^2.$$ I wasn't quite sure how to start on this problem, as factoring out $y^2$ would likely give me a headache and mean that I would have to deal with nasty fractions. I also…
smythe0173
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Finding a quadratic equation given range and vertex to origin distance

The question : "Find the equation of quadratic function that value positive for $-7 < x < 1$ and the distance of vertex and origin is 5" I've just tried to let $-7$ and $1$ are the $x$-intercepts, however, nothing works. Could someone help me,…
Wilory Lu
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Algebraic manipulation of a quadratic equation to an alternative form

I have a quadratic equation that I have attempted to manipulate algebraically but still don't have a reasonable solution. Given a quadratic equation as follows $a(x-k)^2 + b(k-c)^2$ how could this be expressed in the form $d(e-k)^2 + f$ such that…
qboomerang
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