Question

Factorization in proof by induction

score 102 · Answer 1 · 2019-10-11 17:36:59

102

Views

Factorization in proof by induction

Published on 11 Oct 2019 - 17:36

score 955 · Answer 2 · 2026-03-25 04:43:36

955

Views

Find the range of values of $k$ for which $kx^2 + 8x + k <6$ for all real values of $k$

Published on 25 Mar 2026 - 4:43

score 36 · Answer 3 · 2019-10-12 16:55:41

36

Views

Solve for x for the following description

Published on 12 Oct 2019 - 16:55

score 101 · Answer 4 · 2019-10-12 22:46:45

101

Views

Find the number of real solutions of the equation $2^x+x^2=1$

Published on 12 Oct 2019 - 22:46

score 1.1k · Answer 5 · 2019-10-13 04:30:58

1.1k

Views

The polynomial $x^{2k}+1+(x+1)^{2k}$ is not divisible by $x^2+x+1$. Find the value of $k \in \mathbb N$.

Published on 13 Oct 2019 - 4:30

score 3.1k · Answer 6 · 2026-02-23 10:48:58

3.1k

Views

Find a such that $ax^{17}+bx^{16}+1$ is divisible by $x^2-x-1$.

Published on 23 Feb 2026 - 10:48

score 62 · Answer 7 · 2019-10-13 15:01:07

62

Views

How to prove that $ B = A^{-1} $ ? If A and B are 2 x 2 matrices where $ B \neq I_2 $ such that $ ( A + B )^2 = A^2 + 2AB + B^2 $

Published on 13 Oct 2019 - 15:01

score 63 · Answer 8 · 2019-10-14 21:20:03

63

Views

Solve for k, $f(x)=x^2+2(k-1)x+k+5, k\in R$

Published on 14 Oct 2019 - 21:20

score 916 · Answer 9 · 2019-10-14 22:35:04

916

Views

Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has

Published on 14 Oct 2019 - 22:35

score 123 · Answer 10 · 2019-10-15 07:40:34

123

Views

Graph of $x^2$ + $y$ $=$ $0$ is an upward or a downward opening parabola?

Published on 15 Oct 2019 - 7:40

score 69 · Answer 11 · 2019-10-15 10:32:54

69

Views

Find $a\in \mathbb{R}$ for which $a\cdot \left(\frac{1}{1+x^2}\right)^2-3\cdot\frac{a}{1+x^2}+1=0$ will have all roots imaginary

Published on 15 Oct 2019 - 10:32

score 128 · Answer 12 · 2019-10-15 19:18:43

128

Views

$\{a^3+(1-\sqrt{2})a^2-(3+\sqrt{2})a+3\sqrt{2}\}x^2+2(a^2-2)x+a>-\sqrt{2}$

Published on 15 Oct 2019 - 19:18

score 104 · Answer 13 · 2019-10-16 15:12:42

104

Views

If $a^2+c^2>ab$ and $b^2>4c^2$ , for real x, show that $\frac{x+a}{x^2+bx+c^2}$ cannot lie between two limits

Published on 16 Oct 2019 - 15:12

score 86 · Answer 14 · 2019-10-17 01:00:24

86

Views

If $x^5-bx^3+cx^2+dx-e$ can be expressed as the product of a perfect square and a perfect cube then prove following

Published on 17 Oct 2019 - 1:00

score 118 · Answer 15 · 2019-10-17 03:17:46

118

Views

If each pair of equations $x^2=b_1x+c_1=0,x^2=b_2x+c_2 \text{ and } x^2+b_3x=c_3$ have a common root, prove following

Published on 17 Oct 2019 - 3:17

List Question

Factorization in proof by induction

Find the range of values of $k$ for which $kx^2 + 8x + k <6$ for all real values of $k$

Solve for x for the following description

Find the number of real solutions of the equation $2^x+x^2=1$

The polynomial $x^{2k}+1+(x+1)^{2k}$ is not divisible by $x^2+x+1$. Find the value of $k \in \mathbb N$.

Find a such that $ax^{17}+bx^{16}+1$ is divisible by $x^2-x-1$.

How to prove that $ B = A^{-1} $ ? If A and B are 2 x 2 matrices where $ B \neq I_2 $ such that $ ( A + B )^2 = A^2 + 2AB + B^2 $

Solve for k, $f(x)=x^2+2(k-1)x+k+5, k\in R$

Find all real values of the parameter a for which the equation $x^4+2ax^3+x^2+2ax+1=0$ has

Graph of $x^2$ + $y$ $=$ $0$ is an upward or a downward opening parabola?

Find $a\in \mathbb{R}$ for which $a\cdot \left(\frac{1}{1+x^2}\right)^2-3\cdot\frac{a}{1+x^2}+1=0$ will have all roots imaginary

$\{a^3+(1-\sqrt{2})a^2-(3+\sqrt{2})a+3\sqrt{2}\}x^2+2(a^2-2)x+a>-\sqrt{2}$

If $a^2+c^2>ab$ and $b^2>4c^2$ , for real x, show that $\frac{x+a}{x^2+bx+c^2}$ cannot lie between two limits

If $x^5-bx^3+cx^2+dx-e$ can be expressed as the product of a perfect square and a perfect cube then prove following

If each pair of equations $x^2=b_1x+c_1=0,x^2=b_2x+c_2 \text{ and } x^2+b_3x=c_3$ have a common root, prove following

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