Question

Prove: if $px^2 - (p+q)x + p = 0$ has an integer root, $px^2 + qx + p^2 - q = 0$ has an integer root too, for coprime $p,q \in \mathbb{N}$

score 194 · Answer 1 · 2026-04-02 07:55:57

194

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Prove: if $px^2 - (p+q)x + p = 0$ has an integer root, $px^2 + qx + p^2 - q = 0$ has an integer root too, for coprime $p,q \in \mathbb{N}$

Published on 02 Apr 2026 - 7:55

score 30 · Answer 2 · 2026-04-02 07:58:43

30

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score 375 · Answer 3 · 2026-03-26 16:09:45

375

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69

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score 144 · Answer 5 · 2026-04-01 14:30:42

144

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score 68 · Answer 6 · 2020-01-16 14:08:02

68

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score 72 · Answer 7 · 2020-01-16 22:31:04

72

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score 77 · Answer 8 · 2020-01-16 22:48:26

77

Views

Show: For every $\alpha \in \mathbb{Q}$, the polynomial $X^2+\alpha$ has endless different roots in $\mathbb{Q}^{2\times2}$.

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score 80 · Answer 9 · 2020-01-17 04:33:25

80

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score 247 · Answer 10 · 2020-01-17 08:02:39

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score 141 · Answer 11 · 2026-03-29 19:33:04

141

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score 104 · Answer 12 · 2026-04-01 02:07:18

104

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score 469 · Answer 13 · 2026-03-25 17:40:47

469

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Published on 25 Mar 2026 - 17:40

score 94 · Answer 14 · 2020-01-19 14:26:06

94

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Published on 19 Jan 2020 - 14:26

score 76 · Answer 15 · 2020-01-20 20:26:20

76

Views

Find the nature of the roots of the following quartic function:

Published on 20 Jan 2020 - 20:26

List Question

Prove: if $px^2 - (p+q)x + p = 0$ has an integer root, $px^2 + qx + p^2 - q = 0$ has an integer root too, for coprime $p,q \in \mathbb{N}$

Quadratic equation property

Amount of real and complex roots of a polynomial?

solve transcendental equation

Polynomial of degree 4 over $\mathbb{F}_2$ has a root in $\mathbb{F}_{16}$

Polynomial of squares vs polynomial of square root

Finding Zeros of a Specific Function

Show: For every $\alpha \in \mathbb{Q}$, the polynomial $X^2+\alpha$ has endless different roots in $\mathbb{Q}^{2\times2}$.

Is there any non-constant polynomial satisfying $f(1) = f(2) = 0$?

Wolfram alpha, third root of unity

The $n$th root of positive integers has a limit

Inverse of a matrix in $\mathbb{F}_5^{4\times4}$

How to determine number of roots and what type for quartic equations?

Transforming $x^2-x-1=0$ into $(x^2-1)^2-1=x$ introduces roots that don't solve the original equation. What's wrong with the logic?

Find the nature of the roots of the following quartic function:

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