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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How to solve this equation involving two unknowns?

I want a solution of the following equation : $$m^2+n^2-2mn-m=0$$ with the following constraint : $$0n$$
user21982
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How do you find the average rate of change over an interval that is a compound inequality?

Let $f(x)=0.7x^2$ and $g(x)=2.8x^2$. How do I find the average rate of change over $f(x)$ and $g(x)$ over the interval $[4,8]$?
blegh
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Quadratics - Sum of areas is minimum...

I am trying to help my daughter with this question: A piece of wire 12 cm long is cut into 2 pieces. One piece is used to form a square and the other a rectangular shape in which the length is twice its width. a. If x cm is the side length of the…
Rosie Smith
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How to get the solution of (\alpha Z-\ Omega) from the following two equations?

I have the following two equations $$-\frac{\gamma+2P}{1+2Z}[Z^2+(\alpha Z-\Omega)^2]+2(P-\gamma z)[Z+\alpha(\alpha Z-\Omega)]=0$$ (1) $$2Z[-2\gamma_1\frac{\gamma+2P}{1+2Z}Z+Z^2+(\alpha Z-\Omega)^2]-2\gamma_1^2…
Udichi
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Quadratic Formula: Any Shortcomings?

I was wondering, if when solving a quadratic equation where factoring wasn't helpful in finding a solution, if there were any cases in which using the quadratic formula would generate results that would not solve the equation? My understanding is…
Rich S
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Can't understand this quadratic-trinomial-esque equation

the question was this if $x^2 -8x + 7 = (x - a)^2 - b$ then the values of $a$ and $b$ are (Multi choice) the answer was $a = 4, b = 9$ and I don't understand why Here was my work process I expanded so it was $x^2 - 8x + 7 = x^2 - 2ax + a^2 -…
the epic
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How to solve the above question from quadratic equations?

If $a$ and $b$ are the roots of the equation $x^{2}$$-$7$x$$-$1$=$0, then find the value of $($$a^{21}$$+$$b^{21}$$+$$a^{17}$$+$$b^{17}$$)$$/$$($$a^{19}$$+$$b^{19}$$)$$?$ I am trying this question by taking $a^{17}$ common from…
Shivam Kumar
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Find the total of whole roots of the equation below

For how many real values of the number does the equation $x^2+ax+6a=0$ have only integer roots? Putting it in wolfram it shows $18$ roots but I couldn't demonstrate Perfect square: $\Delta = a^2-24a = k^2$? Real Roots: $\Delta = a^2-24a \geq 0…
peta arantes
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Simultaneous Inequality Solving

This originally was a quadratic question with $f(x)=ax^2 + bx + c$ If $1 ≤ a + b + c ≤ 2$ {f(1)} $2 ≤ 4a + 2b + c ≤ 3$ {f(2)} $3 ≤ 9a + 3b +c ≤ 4$ {f(3)} Prove $1 ≤ 16a + 4b + c ≤ 8$ {f(4)} I think I got the limit of why it is $1$, but as for $8$ I…
user1197032
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Without solving the quadratic equation find $x_1^2 - x_2^2$

So i'm doing some problems from quadratic equations, this one in particular is supposed to be solved with vieta's formulas, I'm quite lost at what to do since there is a minus here, for example in solving $x_1^2+x_2^2$ for the same equation, its…
Rahz
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Is this a quadractic function?

A quadratic function can assume this form: $$ q(x) = x^{T}Gx + x^{T}c $$ Taking that into consideration is this a quadratic function? $$ 2{x_{1}}^2 + 3x_{1}{x_{2}}^2 + 6{x_{1}^{2}}x_{2} + {x_{2}}^2 + 4x_{1}x_{2} + x_{2}$$ Having ${x_{2}}^2$ and…
Scipio
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Finding the minimum value of a function using quadratic.

So here, I have the following $$ f(x) = 4^x + 2^x + 1 $$ Now I tried to find the minimum value by doing $y = f(x)$, then doing $4^x + 2^x + 1 - y = 0$, which I solve with the $D \geq 0 $, since this is a real quadratic. This gives me $y \in…
SomeRandomGuyOnTheInternet
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Derivation of Axis of Symmetry from Quadratic Equation in Standard Form

Does the following count as a valid derivation of the axis of symmetry? ${ax}^2+bx+c=0$ $\longrightarrow\ a\left(\frac{ax^2}{a}+\frac{bx}{a}\right)+c=0$ $\longrightarrow\…
FreeThought
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Quadratic equation geometry word problem - lowest value

I have a question that has two parts: The first part is relatively straightforward, this is my approach to part a: However, for part b, I am unsure as to how to approach the problem. I can see that the resulting equation for the area of the sum of…
The Water Tap
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$p$ and $q$ are solutions of the equation $x^2 +p*x+ q=0$. Find values $p$ and $q$.

Given that $p,q$ are roots of the equation $x^2+p*x+q=0$. Find values $p$ and $q$. One method of finding a solution is using Viète’s Theorem. So, $p+q=-p$ and $p*q=q$ and there are two solutions $p=0, q=0$ and $p=1, q=-2.$ Another method is…
TwoTea
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