Question

Let p(x) be a quadratic polynomial such that distinct reals a and b ,. p(a)=a and p(b)=b then find the roots of. p[p(x)]-x=0

score 1k · Answer 1 · 2020-03-19 09:08:58

1k

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Let p(x) be a quadratic polynomial such that distinct reals a and b ,. p(a)=a and p(b)=b then find the roots of. p[p(x)]-x=0

Published on 19 Mar 2020 - 9:08

score 84 · Answer 2 · 2020-03-19 16:41:37

84

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Range of $f(x) = \frac{\sin^2 x + \sin x - 1}{\sin^2 x - \sin x + 2} $

Published on 19 Mar 2020 - 16:41

score 3.1k · Answer 3 · 2020-03-20 04:46:32

Let $<a_n>$ and $<b_n>$ be the arithmetic progression sequences each with common difference 2 such that $a_1<b_1$...

score 54 · Answer 4 · 2026-03-25 06:06:50

54

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Find κ and λ $\in R$ for which $\frac {x^2+κx+λ}{x^2+1} \leq 2$ for all $x \in R$.

Published on 25 Mar 2026 - 6:06

score 759 · Answer 5 · 2020-03-20 14:22:12

759

Views

Number of distinct solutions $(x,y)$ of a system of equations

Published on 20 Mar 2020 - 14:22

score 99 · Answer 6 · 2026-04-01 17:51:06

99

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Find the sum of all positive integers $k$ for which $5x^2-2kx+1<0$ has exactly one integral solution.

Published on 01 Apr 2026 - 17:51

score 2.4k · Answer 7 · 2020-03-21 04:41:56

Let $x_1$ and $x_2$ be the real root of the equation $x^2-kx+(k^2+7k+15)=0$, if the maximum value of $(x_1^2+x_2^2)=\dfrac{18}{x}$, then find 'x'

score 470 · Answer 8 · 2020-03-21 04:59:02

Equation $3\sqrt{-2(x+3)}-1=|x+3|+a$ has exactly two real roots, then the maximum possible value of $|[a]|$ is?

score 1.6k · Answer 9 · 2020-03-21 06:13:39

Find the no of digits in the sum of all integral values of a in $[1,100]$ for which following condition satisfies.

score 351 · Answer 10 · 2020-03-21 06:38:23

351

Views

If $(x^2-5x+4)(y^2+y+1)<2y$ for all real $y$, then $x$ belongs to the interval $(2,b)$, then $b$ can be?

Published on 21 Mar 2020 - 6:38

score 937 · Answer 11 · 2020-03-21 07:36:03

If the system of inequalities $3x^2+2x-1<0$ and $(3a-2)x-a^2x+2<0$ possesses a solution, find the least natural number $a$

score 192 · Answer 12 · 2026-03-25 07:42:56

192

Views

Solve $\tan^2(x) - (1+\sqrt3)\tan(x) + \sqrt3 < 0$

Published on 25 Mar 2026 - 7:42

score 61 · Answer 13 · 2020-03-21 17:49:44

61

Views

Solving for $x$ in a (modified) quadratic

Published on 21 Mar 2020 - 17:49

score 364 · Answer 14 · 2020-03-22 15:34:09

364

Views

The graphs of $f(x)=ax^2 +2bx + c$ and $g(x)=5x^2-3bx-a$ meet at some point for all real values of $b$

Published on 22 Mar 2020 - 15:34

score 69 · Answer 15 · 2026-03-30 03:05:22

69

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Find the values of $m\in\mathbb{R}$ such that the equation $x^2-|x|=mx(x+1)$ has exactly $3$ real and distinct solutions.

Published on 30 Mar 2026 - 3:05

List Question

Let p(x) be a quadratic polynomial such that distinct reals a and b ,. p(a)=a and p(b)=b then find the roots of. p[p(x)]-x=0

Range of $f(x) = \frac{\sin^2 x + \sin x - 1}{\sin^2 x - \sin x + 2} $

Let $<a_n>$ and $<b_n>$ be the arithmetic progression sequences each with common difference 2 such that $a_1<b_1$...

Find κ and λ $\in R$ for which $\frac {x^2+κx+λ}{x^2+1} \leq 2$ for all $x \in R$.

Number of distinct solutions $(x,y)$ of a system of equations

Find the sum of all positive integers $k$ for which $5x^2-2kx+1<0$ has exactly one integral solution.

Let $x_1$ and $x_2$ be the real root of the equation $x^2-kx+(k^2+7k+15)=0$, if the maximum value of $(x_1^2+x_2^2)=\dfrac{18}{x}$, then find 'x'

Equation $3\sqrt{-2(x+3)}-1=|x+3|+a$ has exactly two real roots, then the maximum possible value of $|[a]|$ is?

Find the no of digits in the sum of all integral values of a in $[1,100]$ for which following condition satisfies.

If $(x^2-5x+4)(y^2+y+1)<2y$ for all real $y$, then $x$ belongs to the interval $(2,b)$, then $b$ can be?

If the system of inequalities $3x^2+2x-1<0$ and $(3a-2)x-a^2x+2<0$ possesses a solution, find the least natural number $a$

Solve $\tan^2(x) - (1+\sqrt3)\tan(x) + \sqrt3 < 0$

Solving for $x$ in a (modified) quadratic

The graphs of $f(x)=ax^2 +2bx + c$ and $g(x)=5x^2-3bx-a$ meet at some point for all real values of $b$

Find the values of $m\in\mathbb{R}$ such that the equation $x^2-|x|=mx(x+1)$ has exactly $3$ real and distinct solutions.

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