Question

Let $P(x)=x^2+bx+c$, where $b$ and $c$ are integers.

score 332 · Answer 1 · 2026-03-25 06:20:59

332

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Let $P(x)=x^2+bx+c$, where $b$ and $c$ are integers.

Published on 25 Mar 2026 - 6:20

score 372 · Answer 2 · 2018-08-06 14:09:17

372

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If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$

Published on 06 Aug 2018 - 14:09

score 70 · Answer 3 · 2018-08-06 16:12:13

70

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Let $l$ be the minimum value of $2(y-2)^2 +4(x -7)^2 +(y+4)^2$. Find $[2018/l]$ where $[\cdot]$ is the greatest integer function.

Published on 06 Aug 2018 - 16:12

score 279 · Answer 4 · 2026-03-26 21:10:32

279

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If the roots of the equation $ax^2-2bx+c=0$ are complex ,then find the number of real roots of the equation $4e^x+(a+c)^2(x^3+x)=4b^2x$.

Published on 26 Mar 2026 - 21:10

score 140 · Answer 5 · 2026-03-25 03:07:30

140

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Is there a zeta function(with a Dirichlet series) having known roots off the critical line?

Published on 25 Mar 2026 - 3:07

score 367 · Answer 6 · 2026-03-25 13:58:08

367

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Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Published on 25 Mar 2026 - 13:58

score 1k · Answer 7 · 2018-08-07 14:15:34

1k

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Some interesting observations on a sum of reciprocals

Published on 07 Aug 2018 - 14:15

score 1.6k · Answer 8 · 2026-03-24 19:01:23

1.6k

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How many zeros does the polynomial have in the right half plane?

Published on 24 Mar 2026 - 19:01

score 149 · Answer 9 · 2026-03-25 04:35:15

149

Views

Construct an analytic function which has simple zeros at all $m+in$

Published on 25 Mar 2026 - 4:35

score 269 · Answer 10 · 2026-03-29 04:41:42

269

Views

Constant Term of a Monic Polynomial in $\mathbb{Z}[x]$ Is Divisible by 3

Published on 29 Mar 2026 - 4:41

score 3.6k · Answer 11 · 2018-08-09 21:10:45

3.6k

Views

Why can you find the roots a of polynomial by factoring it?

Published on 09 Aug 2018 - 21:10

score 625 · Answer 12 · 2026-03-25 04:57:31

625

Views

Proof of Casorati-Weierstrass

Published on 25 Mar 2026 - 4:57

score 75 · Answer 13 · 2018-08-10 18:20:43

75

Views

How to find the coefficient of $a$ in a quadratic equation?

Published on 10 Aug 2018 - 18:20

score 110 · Answer 14 · 2018-08-11 03:10:22

Consider $P(x) = 5x^6 - ax^4 - bx^3 - cx^2 - dx - 9$, where $a$; $b$; $c$; $d$ are real. If the roots of $P(x)$ are in AP, find the value of $a$.

score 334 · Answer 15 · 2018-08-11 04:48:33

334

Views

The root sign and it's relation with 1/2.

Published on 11 Aug 2018 - 4:48

List Question

Let $P(x)=x^2+bx+c$, where $b$ and $c$ are integers.

If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$

Let $l$ be the minimum value of $2(y-2)^2 +4(x -7)^2 +(y+4)^2$. Find $[2018/l]$ where $[\cdot]$ is the greatest integer function.

If the roots of the equation $ax^2-2bx+c=0$ are complex ,then find the number of real roots of the equation $4e^x+(a+c)^2(x^3+x)=4b^2x$.

Is there a zeta function(with a Dirichlet series) having known roots off the critical line?

Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$

Some interesting observations on a sum of reciprocals

How many zeros does the polynomial have in the right half plane?

Construct an analytic function which has simple zeros at all $m+in$

Constant Term of a Monic Polynomial in $\mathbb{Z}[x]$ Is Divisible by 3

Why can you find the roots a of polynomial by factoring it?

Proof of Casorati-Weierstrass

How to find the coefficient of $a$ in a quadratic equation?

Consider $P(x) = 5x^6 - ax^4 - bx^3 - cx^2 - dx - 9$, where $a$; $b$; $c$; $d$ are real. If the roots of $P(x)$ are in AP, find the value of $a$.

The root sign and it's relation with 1/2.

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