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Show that the roots of the equation $x^2-4abx+(a^2+2b^2)^2=0$ are imaginary.

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#polynomials #roots #quadratics
229
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If $a$, $b$, $c$ are rational and $a+b+c=0$, show that the roots of $(b+c-a)x^2 + (c+a-b)x + (a+b-c)=0$ are rational.

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#polynomials #roots #quadratics
65
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Dimensions that give maximum volum of a box

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#derivatives #quadratics #volume
6.8k
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Prove that the roots of the equation $(x-a)(x-b)=k^2$ are real for all values of k.

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#polynomials #roots #quadratics
76
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Algebra (inequalities)

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#algebra-precalculus #inequality #quadratics #a.m.-g.m.-inequality
2.4k
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When is this integer a perfect square: $n^2 + 20n + 12$

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#elementary-number-theory #contest-math #quadratics #integers #square-numbers
179
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Inverse function to $f(x)=\frac{e^x-e^{-x}}{2}$

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#algebra-precalculus #exponential-function #inverse #quadratics #hyperbolic-functions
560
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Quadratic equation with equal roots

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#algebra-precalculus #polynomials #quadratics
180
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Formation of quadratic equation using roots

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#quadratics
58
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Range of variables

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#polynomials #optimization #quadratics #maxima-minima
94
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Quadratic Simultaneous equation

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#systems-of-equations #quadratics
100
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Equation solving involving terms inside roots

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#quadratics
328
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Finding integer coefficients in a quadratic equation

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#roots #quadratics
345
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For some integers a and b, the same integer satisfies both of the equations, what is the greatest possible value?

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#elementary-number-theory #quadratics #integers
42
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Calculating the equation of a parabola by its coordinates

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#quadratics

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