Embibe Experts Solutions for Chapter: Theory of Equations, Exercise 1: TS EAMCET 2018 (04-May Shift-1)

The equation whose roots are squares of the roots of $x^4-2x^3+6x-21=0$ is

If $f\left(x\right)=x^2+ax+2=0$ and $g\left(x\right)=x^2+2x+a=0$ have only one real common root, then sum of the roots of $f\left(x\right)+g\left(x\right)=0$ is

$f\left(x\right)=a{x}^2-bx-a$ is a quadratic expression. If $K$ is the least real number such that $f\left(x\right)\le K, \forall x\in R,$ then

If $x^2-5x-14>0\Rightarrow x$ lie outside $[\alpha , \beta ],$ then $\frac{\alpha }{\beta }=$

If $\alpha , \beta , \gamma$ are the roots of $x^3-x+1=0,$ then $\frac{1+\alpha }{1-\alpha }+\frac{1+\beta }{1-\beta }+\frac{1+\gamma }{1-\gamma }=$

If $x=2+2^{\frac{2}{3}}+2^{\frac{1}{3}},$ then $x^3-6x^2+6x=$

The roots of the cubic equation $3x^3+4x^2-5x-2=0$ are diminished by $h,$ and a cubic equation with these diminished roots is formed. If the transformed equation does not contain $x^2$ term, then the roots of the transformed equation are

If the roots of the equation $3x^3-26x^2+52x-24=0$ are in geometric progression, then the sum of two of its roots is