Question

How do I compute the minimum or maximum LINE of a bivariate quadratic function?

score 54 · Answer 1 · 2026-03-25 15:59:22

54

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How do I compute the minimum or maximum LINE of a bivariate quadratic function?

Published on 25 Mar 2026 - 15:59

score 155 · Answer 2 · 2026-04-15 21:21:24

155

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conditions an $a,b,c,d$ so that $z^2+az+b=0,z^2+cz+d=0$ are collinear .

Published on 15 Apr 2026 - 21:21

score 64 · Answer 3 · 2026-04-12 21:43:31

64

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Why can any quadratic equation be reduced to the product of its two factors involving the roots?

Published on 12 Apr 2026 - 21:43

score 2.3k · Answer 4 · 2026-04-22 15:35:34

2.3k

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Questions about a trick for solving quadratic equations quickly

Published on 22 Apr 2026 - 15:35

score 127 · Answer 5 · 2026-04-22 15:32:31

127

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Factorize $abx^2-(a^2+b^2)x+ab$

Published on 22 Apr 2026 - 15:32

score 120 · Answer 6 · 2026-04-16 04:02:30

120

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Determine the sign of $169\cdot7-49\sqrt{123}$

Published on 16 Apr 2026 - 4:02

score 85 · Answer 7 · 2026-04-12 20:10:11

85

Views

We all know about linear algebra; but does a 'quadratic algebra' exist as well?

Published on 12 Apr 2026 - 20:10

score 567 · Answer 8 · 2026-04-12 21:59:25

567

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A biquadratic equation to have at least two real roots

Published on 12 Apr 2026 - 21:59

score 101 · Answer 9 · 2026-04-15 14:33:52

101

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How to find the points of intersection in a curve and a line

Published on 15 Apr 2026 - 14:33

score 31 · Answer 10 · 2026-04-12 10:40:40

31

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Conditions on coefficients obtained when solving two equations

Published on 12 Apr 2026 - 10:40

score 76 · Answer 11 · 2026-04-17 14:02:11

76

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Given that $a+b = c+d = 10$ and $|a-b| > |c-d|$, show that $ab<cd$

Published on 17 Apr 2026 - 14:02

score 62 · Answer 12 · 2026-04-15 23:25:16

62

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Find $k$ for real solutions of quadratic equation $\sin^4 x + 2(1 + k)\sin^2 x- k - 2 = 0$

Published on 15 Apr 2026 - 23:25

score 150 · Answer 13 · 2026-04-17 05:41:35

150

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Solving $x^2-\lfloor x\rfloor -4=0$

Published on 17 Apr 2026 - 5:41

score 53 · Answer 14 · 2026-04-17 10:48:06

$x^2 +2ax+b=0$ where $x_1$ and $x_2$ are real solutions. For which value of $b$ function $f(b)=|x_1-x_2|$ reaches maximum if $|x_1-x_2|=2m$

score 67 · Answer 15 · 2026-04-16 00:17:15

How to think while solving question like this? If $ax^2+bx+c=0$ has roots $A$ and $A^n$, then $(ac^n)^{1/(n+1)}+(a^nc)^{1/(n+1)}+b=0$.

List Question

How do I compute the minimum or maximum LINE of a bivariate quadratic function?

conditions an $a,b,c,d$ so that $z^2+az+b=0,z^2+cz+d=0$ are collinear .

Why can any quadratic equation be reduced to the product of its two factors involving the roots?

Questions about a trick for solving quadratic equations quickly

Factorize $abx^2-(a^2+b^2)x+ab$

Determine the sign of $169\cdot7-49\sqrt{123}$

We all know about linear algebra; but does a 'quadratic algebra' exist as well?

A biquadratic equation to have at least two real roots

How to find the points of intersection in a curve and a line

Conditions on coefficients obtained when solving two equations

Given that $a+b = c+d = 10$ and $|a-b| > |c-d|$, show that $ab<cd$

Find $k$ for real solutions of quadratic equation $\sin^4 x + 2(1 + k)\sin^2 x- k - 2 = 0$

Solving $x^2-\lfloor x\rfloor -4=0$

$x^2 +2ax+b=0$ where $x_1$ and $x_2$ are real solutions. For which value of $b$ function $f(b)=|x_1-x_2|$ reaches maximum if $|x_1-x_2|=2m$

How to think while solving question like this? If $ax^2+bx+c=0$ has roots $A$ and $A^n$, then $(ac^n)^{1/(n+1)}+(a^nc)^{1/(n+1)}+b=0$.

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