Embibe Experts Solutions for Exercise 1: EXERCISE 5.1

If $\alpha$ and $\beta$ are the roots of the equation $x^2+6x+\lambda =0$ and $3\alpha +2\beta =-20,$ then $\lambda =$

The quadratic equation having rational co-efficients, whose one root is $\frac{1}{2+\sqrt{5}}$ will be

A value of $k$ for which the quadratic equation $x^2-2x(1+3k)+7(2k+3)=0$ has equal roots is

If every pair of the equations $x^2+px+qr=0,x^2+qx+rp=0,x^2+rx+pq=0$ have a non-zero common root, then the sum of three common roots is

If the product of the roots of the equation $\left(a+1\right)x^2+\left(2a+3\right)x+\left(3a+4\right)=0$ be $2,$ then the sum of roots is

If $\alpha$ and $\beta$ are the roots of the equation $a{x}^2+bx+c=0$ then the equation whose roots are $\alpha +\frac{1}{\beta }$ and $\beta +\frac{1}{\alpha }$ is

If $\alpha$ and $\beta$ are the roots of the equation $x^2-7x+1=0$ then find the value of $\frac{1}{(\alpha -7{)}^2}+\frac{1}{(\beta -7{)}^2}$.

Find the sum of all real roots of the equation $(x-2{)}^2+|x-2|-2=0$.