Embibe Experts Solutions for Chapter: Theory of Equation, Exercise 1: KEAM 2018

The number of values of $a$ for which $\left(a^2-3a+2\right)x^2+\left(a^2-5a+6\right)x+a^2-4=0$ is an identity in $x$ is

If $\alpha \ne \beta , {\alpha }^2=5 \alpha -3, {\beta }^2=5\beta -3$$,$ then the equation having $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$ as its roots is

Let $f\left(x\right)=p{x}^2+qx+r$$,$ where $p, q, r$ are constants and $p\ne 0.$ If $f\left(5\right)=-3f\left(2\right)$ and $f\left(-4\right)=0$$,$ then the other root of $f$ is

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $a{x}^2+bx+c=0$$,$ then

The solutions of $x^{\frac{2}{5}}+3x^{\frac{1}{5}}-4=0$ are

If the equations $x^2+ax+1=0$ and $x^2-x-a=0$ have a real common root $b$$,$ then the value of $b$ is equal to

$(7-4\sqrt{3}{)}^{x^2-4x+3}+(7+4\sqrt{3}{)}^{x^2-4x+3}=14$ then $x=?$

If the roots of $x^3-12x^2+39x-28=0$ are in AP, then their common difference is