Embibe Experts Solutions for Chapter: Theory of Equations, Exercise 1: AP EAPCET - 20 Aug 2021 Forenoon

If $\alpha ,\beta$ are the roots of $11x^2+12x-13=0$, then $\frac{1}{{\alpha }^2}+\frac{1}{{\beta }^2}=$? (approximately close to)

If one root of the equation $i{x}^2-2(i+1)x+(2-i)=0$ is $(2-i)$, then the other root is

If $2,1,1$ are roots of the equation $x^3-4x^2+5x-2=0$, then the roots of ${\left(x+\frac{1}{3}\right)}^3$ $-4{\left(x+\frac{1}{3}\right)}^2+5\left(x+\frac{1}{3}\right)-2=0$

$2+\sqrt{5},1$ are roots of the cubic equation given by

If $a$ is a positive integer such that the roots of the equation $7x^2-13x+a=0$ are rational numbers, then the smallest possible value of $a$ is

For $a\ne b$, if the equation $x^2+ax+b=0$ and $x^2+bx+a=0$ have a common root, then the value of $a+b=$

Given $\frac{3x-2}{(x+1{)}^2(x+3)}=\frac{A}{x+1}+\frac{B}{(x+1{)}^2}+\frac{C}{x+3}$, then $4A+2B+4C$

If the product of the roots of $9x^3+112x^2-120x+a=0$ is $12$ , then the value of  ${}^{\text{'}}a^{\text{'}}$ is