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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Asymptotic behavior of a solution to the quadratic equation

I have a quadratic equation of real $x$, $$ x^2 - 4(1+2y)x + 8(y+1) = 0 $$ for $ x>0, y>0$ and the solution is $$ x(y) = 4y + 2 - \sqrt{4(1+2y)^2 - 8(y+1)} $$ $$ = 4y + 2 - 2\sqrt{4y^2 + 2y -1} $$ I found the solution approaches to 1 for large $y$,…
ben Heo
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Solve quadratic with unknown constant in question

The quadratic equation $2x^2-px-4=0$ where $p$ is a positive constant, has 2 solutions that differ by 6. What is the value of $p$? I attempted to factorise to get (2x-2)(x+2)=0 and (2x-4)(x+1)=0 but the solutions don’t differ correctly.
b0018877
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The sum of the values of a for which $\frac{x^3-6x^2+11x-6}{x^3+x^2-10x+8} + \frac a{30} = 0$ does not have a real solution is

The sum of the values of a for which $$\frac{x^3-6x^2+11x-6}{x^3+x^2-10x+8} + \frac a{30} = 0$$ does not have a real solution is A. $1$ B. $12$ C. $13$ D. $2$ I tried to factorise the numerator and the denominator and…
Neetu Yadav
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Help me with this quadratic equation where the roots ia prime number

If $x^2-2013x+c=0$ and the both roots of this equation is prime numbers, what is the possible number for $^3√c$?
ilham maha
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If $\alpha, \beta$ roots of the equation $ax^2+by+c=0$. Then find the value of

$$\frac{1}{(a\alpha+b)^2}+\frac{1}{(a\beta+b)^2}$$ I can solve it by simplifying everything, but it will obviously we very long. How should I shorten my calculations? Answer is $\frac{b^2-2ac}{c^2a^2}$
Aditya
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Prove $1/x + 1/y = 0$ is not linear.

I was trying to complete an exercise of a book and tried to solve this question but wasn't able to succeed. I searched it on google but found no results related to this question. Please help.
Ritanshu Singh
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A free website which can solve this equation

Am looking for a website which can solve quadratic equations such this solve for $v$ , $h(v-t) = h(v+t) $ where $h(x) = ax^2 + bx +c$. The value is the vertex of the quadratic function the website wolfarmalpha can solve that when $a,b$ and $c$ are…
IrbidMath
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Why do I have to multiply the 2 on both sides?

This is from completing the square practice on Khan Academy. Why do we multiply the 2 on the right side? Why not just subtract 121/16.
artdensity
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Quadratic equation - finding $x$ given $y$ value

I've been having trouble with this quadratic equation where $6639.55 = -0.06493x^2 + 22.35175x + 5065.25$. My question is, how do I find out $x$? Thank you in advance for any advice!
rsfan23
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Quadratic Yield Response Function

How do I find the quadratic yield response function in the form of "$Y = b_0 + b_1X+ b_2X^2$" for a set of data in excel?
Cody Rutscher
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Quadratic equations confusion

Well we know about quadratic equations, but quad means four, but quadratic equations have two roots. So why is it so?
Shamim Akhtar
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How to reverse formula $S = \frac{n(n+1)}{2}$

I'm using this formula $S = \frac{n(n+1)}{2}$ to calculate sum of numbers from 1 to $n$. But, I want to recover $n$ value. If I have $S$ value. Is it possible? If yes, please provide that formula. Thanks.
Temüjin
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What is the value of $t$?

$$x^2 -tx +9=0 $$ The second root of this equation is given as $1$. What is the value of $t$? Unfortunalety, I'm stuck at this problem. I'm getting $t = \pm 10$ for $x = 1$ However, the right answer seems $\frac {25}{4}$ UPDATE: The second root…
Goendo
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Possible real values

Set of all possible real values of a such that the inequality $(x-(a-1))(x-(a^2+2))<0$ holds for all $x$ belongs to $(1,3)$ needs to be found. I tried by putting $x=2$ in the inequality, but nothing good resulted. I thought I would get the idea but…
user532267
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What would the roots be for this quadratic equation $f(x)=2x^2-6x-8$?

I am an 10 grade high school student. I really need help on this problem, my teacher was out today and i need help on completing this problem. Thank you.
Mikester
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