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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Eliminate variable x from 2 quadratic equations

The two quadratic equations which I have are $x^2 - 1970x + 10a =0 $ and $87x^2 - 3600x + 10b = 0$ I need to eliminate x from these equations such that I get a relation between $a$ and $b$. How shall I do it ?
ShiS
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find the Roots of this equation

The roots of the equation $x^{4} -2x^{3} + x = 380$ are: Though by trial and error one could solve the question, but I wanted to now if there is a particular method for solving the above equation ?
ShiS
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Conditions for an expression to be a perfect square

Find the relation in $a,c$ and $d$ so that $$(x^4 + ax^3 + bx^2 + cx + d)$$ is perfect square where $a,b,c,d \in \mathbb{R}$
Anshuman Kumar
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How to expand equations with more number of bracket operations?

How can I solve and expand the equation which have more number of brackets ? Since opening and performing the operation on single brackets becomes a tedious task. Is there any other method which can be used to expand the equations and finding the…
DaSnipeKid
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Quadratic Equation Problem....

I am stuck on this problem: If $\sqrt{x^2+4ax+5}+\sqrt{x^2+4bx+5}=2(a-b)$ then $x=?$ I did the following things 1) For solution to exist a≥b 2) $x^2+4ax+5≥0$ which implies that $16a^2-20≤0$ On differentiating the quadratic $x^2+4ax+5=0$, I get…
Arishta
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Quadratic Algebra Help

The graph of the function f(x) = ax^2+bx+c contains the points (p - q, q), (p, -2q), and (p+q, q) with q =/= 0. Determine a, b, and c in terms of p's and q's. I have no idea how to do this, please help! An explanation of how to get to the answer…
xpoporo
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solving $y=4/x+\sqrt{x+0.2−5x}$

it's actually $y=\frac{4}{x}+\sqrt{x+0.2-5x}$ (see algebra problem) $$y=\frac{4}{x}+\sqrt{x+0.2-5x}$$ if $x=\frac45$ what is y?
user329008
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Find $p$ and $q$ for $y(x)=x^2+px+q$.

Find $p$ and $q$ for $y(x)=x^2+px+q$ if the function has minimum equal to $-4$ for $x=1$ Can anyone try to solve this please?
Marko Pranjić
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Solving a quadratic involving square root

$$\sqrt{\frac{x}2} = 1-x$$ so $$x = ?$$ I have tried to solve many times and i got $x = \frac52$ everytime. But my book says answer is $\frac12$. I think i couldn't understand square roots clearly.. So, Where is my mistake ? Give me a hint or show…
Oğuz İsmayil uysal
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Constructing a quadratic equation

So basically I have been assigned a question that involves constructing a quadratic equation from scratch and graphing it. So here are the details. We are designing a water arc fountain, and it has a maximum of $20$ feet wide and taller than $6$…
Majid Alshamsi
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Story problem using quadratic formula

The pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of the water t seconds after its release is modeled by $y = -16t^2 - 2t + 400$. The horizontal distance $x$ in feet between the water and its point…
Desiree
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Solve the equation. Give the solutions as EXACT numbers

I have to following problem: $$q²+3q=40$$. The anwser is $q=5$ and $q= −8$ can someone give me the steps?
ZZZ2001
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Number of distinct solutions $(x,y)$ of a system of equations

Let $a\in\mathbb{R}$. The number of distinct solutions $(x,y)$ that satisfy the system of equations $(x-a)^{2}+y^{2}=1$ and $x^{2}=y^{2}$ can only be _____.
Keshav Balwant Deoskar
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Formation of new Quadratic Equation by changing the roots of a given Quadratic Equation.

If $\alpha$ and $\beta$ are the root of equation $ax^2+bx+c=0$. Prove that the equation whose root is $\alpha^n$ and $\beta^n$ is $$a(x^\frac 1n)^2+b(x^\frac 1n)+c=0$$ I had already found the equation whose root is whose root is $\alpha^n$ and…
user470123
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quadratic equation with complex coeeficient

Given that p and q are real and that $1+2i$ is a root of the equation : $$Z^2+(p+5i)z+q(2-i)=0$$ Determine The value of p and q. The other root of the equation.
Adeb GHAYOUR
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