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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Cross section of parabolic satellite in Quadratic Functions

A parabolic satellite dish has a cross section that can be modelled by the equation $$y = 0.05\,x^2.$$ While still in the shipping yard, the dish fills with rain. The rain forms a circular puddle with a diameter of $2$m. What is the depth of the…
Student
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how to solve this quadratic equation

$n^2-4n+2=0$ I have tried many things for this but I cant resolve the roots here $n$ should be a positive whole number as it stands for time.
agha rehan abbas
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How to obtain root of this quadratic equation

I got this quadratic equation in a problem $T^2 - 2T - 40 = 0$, but i am unable to find the roots of this equation. Is any other concept hidden in this equation? Please help. I am basically a Bipc [biology physics and chemistry] student of India and…
agha rehan abbas
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Expressing quadratic equation in terms of its roots

For a quadratic equation, $ax^2 + bx + c = 0$, why is $ax^2 + bx + c = a(x-\alpha)(x-\beta)$ where alpha, beta are the roots of the equation? Why not just $(x-\alpha)(x-\beta)$?
user34304
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Where does the quadratic formula come from?

Everywhere I look, the $ax^2+bx+c$ portion of the quadratic formula is listed as given. Does anyone know where this comes from? Edit How can we prove that (x+y)^2 = ax^2+bx+c?
user156910
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Completing the square with second degree coefficient greater than one

How do I complete the square when the second degree coefficient is greater than one. I can do it when $x^2+4x-4=0$, for example, but I can't work out how to do when $3x^2+4x-4=0$.
Jeremy
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Quadratic equations and probability

The inequality: 4p^2-17p+4>0 Solving using quadratic equation: (−(−17)±√(−17)^2−4⋅4⋅4)/8 =(12±√225)/8 I realize why p = 4 or p = 1/4, and in this case p represents and probability so the solution is 1/4 but how do I know if p is < or > than…
Jeremy
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Inequality involving a quadratic equation

Let $a,b,c$ be integers and suppose the equation $$f(x) = ax^2 + bx + c = 0$$ has an irrational root $r$ . Let $u=\dfrac{p}{q}$ be any rational no. such that $|u-r|<1$. Prove that $$\dfrac{1}{q^2} ≤ |f(u)|≤ K|u-r|$$ for some constant $K$…
Alok Ranjan
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Prove $\alpha^3 + \beta^3 = S^3 - 3PS$ in Quadratic Equation

We have a quadratic equation like this: $ax^2 + bx + c = 0$ and we know that $S = \alpha + \beta = -b/a$ and $P = \alpha\beta = c/a$. How we can prove that $\alpha^3 + \beta^3 = S^3 - 3PS$ and is there any relation to $\alpha^n + \beta^n$?
Amirreza Nasiri
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Quadratic equation problem. Composition of functions

Suppose $p(x)$ and $q(x)$ are quadratic polynomials and the three largest roots of $p(q(x))$ are $10$, $20$ and $23$. What is the smallest root of $p(q(x))$? Then, there will be 4 roots. $q(10)$ $q(20)$ $q(23)$ $q$(another zero) will make the…
most venerable sir
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Why the discriminant determine whether a quadratic has real roots or not?

It's been quiet a mystery for, why is this true:? If $\Delta>0$ then it have two solutions. If $\Delta=0$ then it have only one solution. If $\Delta<0$ then it have no solutions
user149155
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Finding the value of a parameter, when equations have a common root

How can I find the value of the real parameter $m$, if $2x^2-3x+1=0$ and $3x^2+m(x+2)+1=0$ have a common root? I opened the parentheses, got rid of the $x^2$ , but I get a big fraction as the value of the common root. Where did I go wrong?
user130101
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What is the roots for the following equation

Can someone please show me to solve the roots for the following equation $9x^2-8x-1 < 0 $ I am getting the root as below $(x-9)(x+1)$ then getting $x = 9 ,~x = -1$ , which is wrong. I have solved is as follows Multiplication should give the value…
Gaurav_soni
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Ellipse equation. What does it need to be in order for $b > a$?

We have the quadratic equation: $$ax^2 + bx + cy^2 + dy + e$$ $a$ and $c$ are both negative or both positive. How can I, by looking at that only, determine whether $b$ (the length of the semi-minor axis) will be bigger than $a$ (the length of the…
danny
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Find the range of $k$.

Let a, b, c be the sides of a triangle where $a\neq c$ and $k \in R$. If the roots of the equation $x^2+ 2(a + b +c)x + 3k(ab + bc + ca) = 0$ are real, then find the interval in which $k$ lies. I have used the fact that equation has real roots, but…
Kumar
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