Question

Conditions for positive roots for cubic equation

score 53 · Answer 1 · 2026-03-27 01:44:45

53

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Conditions for positive roots for cubic equation

Published on 27 Mar 2026 - 1:44

score 33 · Answer 2 · 2026-04-09 04:25:32

33

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Will $ -a e^{2x} + b e^{x} - cx + d$ always have a root for positive $a,c$?

Published on 09 Apr 2026 - 4:25

score 125 · Answer 3 · 2026-04-03 14:11:14

Given $ax^2+bx+c=0$ with two real roots, $x_1>x_2$, find a quadratic equation whose roots are $x_1+1$ and $x_2-1$ without solving the first equation

score 77 · Answer 4 · 2020-06-16 01:26:08

77

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$P(x)$ has integer coefficients and admits $4$ integer roots. Prove that $P(x) = 2$ does not admit integer roots.

Published on 16 Jun 2020 - 1:26

score 62 · Answer 5 · 2026-04-03 14:09:47

62

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Find all possible values $m$ such that $f(x)=x^2-5mx+10m-4$ has 2 roots and one of them is twice as the other

Published on 03 Apr 2026 - 14:09

score 780 · Answer 6 · 2020-06-17 14:07:46

780

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Value of $\alpha$ for which $x^5+5\lambda x^4-x^3+(\lambda\alpha-4)x^2-(8\lambda+3)x+\lambda\alpha-2=0$ has roots independent of $\lambda$

Published on 17 Jun 2020 - 14:07

score 44 · Answer 7 · 2026-03-27 00:57:02

44

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Finding zeros for $2a + 4bx^2 - qcx^{q-2} $

Published on 27 Mar 2026 - 0:57

score 29 · Answer 8 · 2026-04-09 11:41:59

29

Views

Proving equation has solution for every $c ≥ 0$

Published on 09 Apr 2026 - 11:41

score 103 · Answer 9 · 2020-06-20 15:01:43

103

Views

$3^x+4^x+5^x=6^x$ has exactly one real solution

Published on 20 Jun 2020 - 15:01

score 120 · Answer 10 · 2026-03-27 01:47:00

120

Views

Trigonometric identity of $\cos \left (\frac {\theta}{3}\right)$

Published on 27 Mar 2026 - 1:47

score 562 · Answer 11 · 2020-06-21 00:39:17

562

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Finding all real $a$ such that $16x^4-(a)x^3+(2a+17)x^2−(a)x+16=0$ has four distinct roots in geometric progression

Published on 21 Jun 2020 - 0:39

score 331 · Answer 12 · 2026-03-25 09:28:30

331

Views

Degree of a multivariate polynomial over a finite field with many roots

Published on 25 Mar 2026 - 9:28

score 56 · Answer 13 · 2020-06-22 08:06:54

56

Views

Zeros of polynomial

Published on 22 Jun 2020 - 8:06

score 162 · Answer 14 · 2026-04-09 11:43:28

162

Views

Find quintic roots of $x^ 5 = 1$

Published on 09 Apr 2026 - 11:43

score 77 · Answer 15 · 2026-04-11 11:07:36

77

Views

Auxiliary Angle Cambridge Question

Published on 11 Apr 2026 - 11:07

List Question

Conditions for positive roots for cubic equation

Will $ -a e^{2x} + b e^{x} - cx + d$ always have a root for positive $a,c$?

Given $ax^2+bx+c=0$ with two real roots, $x_1>x_2$, find a quadratic equation whose roots are $x_1+1$ and $x_2-1$ without solving the first equation

$P(x)$ has integer coefficients and admits $4$ integer roots. Prove that $P(x) = 2$ does not admit integer roots.

Find all possible values $m$ such that $f(x)=x^2-5mx+10m-4$ has 2 roots and one of them is twice as the other

Value of $\alpha$ for which $x^5+5\lambda x^4-x^3+(\lambda\alpha-4)x^2-(8\lambda+3)x+\lambda\alpha-2=0$ has roots independent of $\lambda$

Finding zeros for $2a + 4bx^2 - qcx^{q-2} $

Proving equation has solution for every $c ≥ 0$

$3^x+4^x+5^x=6^x$ has exactly one real solution

Trigonometric identity of $\cos \left (\frac {\theta}{3}\right)$

Finding all real $a$ such that $16x^4-(a)x^3+(2a+17)x^2−(a)x+16=0$ has four distinct roots in geometric progression

Degree of a multivariate polynomial over a finite field with many roots

Zeros of polynomial

Find quintic roots of $x^ 5 = 1$

Auxiliary Angle Cambridge Question

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