Embibe Experts Solutions for Chapter: Quadratic Equations, Exercise 2: Exercise

The number of values of $k$ for which $\left[x^2-\left(k-2\right)x+k^2\right]·\left[x^2+kx+\left(2k-1\right)\right]$ is a perfect square is

If $\alpha , \beta , \gamma$ are such that $\alpha +\beta +\gamma =2, {\alpha }^2+{\beta }^2+{\gamma }^2=6, {\alpha }^3+{\beta }^3+{\gamma }^3=8,$ then ${\alpha }^4+{\beta }^4+{\gamma }^4$ is

The number of real solutions of the equation ${\left(\frac{9}{10}\right)}^x=-3+x-x^2$ is

If the equation ${\cot }^{4}x-2{cosec}^{2}x+a^2=0$ has at least one solution then, sum of all possible integral values of $a$ is equal to

If the quadratic equation $4x^2-2\left(a+c-1\right)x+ac-b=0; \left(a>b>c\right)$ is given, then

If the equation $\left|x^2+bx+c\right|=k$ has four real roots, then

$P\left(\mathit{x}\right)$ is a polynomial with integral coefficients such that for four distinct integers $a\mathit{,}\mathit{ }b\mathit{,}\mathit{ }c\mathit{,}\mathit{ }d\mathit{:}P\left(a\right)\mathit{=}P\left(b\right)\mathit{=}P\left(c\right)\mathit{=}P\left(d\right)\mathit{=}3$. If $P\left(e\right)=5$ ($e$ is an integer), then

The value of the expression $x^4-8x^3+18x^2-8x+2$ when $x=2+\sqrt{3}$