Question

Let alpha, beta be the values of m for which the equation (1+m)x2 -2(1+3m)x +(1+8m) has equal roots. Find the equation whose roots are alpha+2 and beta+2.

Answer 1

$\fontsize{18}{10}{\textup}{\textbf{The required equation is x^2-4x+1=0}}$

Step-by-step explanation:

Form the equation with equal roots

Determinant, [2(1+3m)]^2-4(1+m)(1+8m)=0

4+36m^2+24m-4-32m^2-36m=0

4m^2-12=0

m^2=3

m=+-rt3

therefore the values of alpha and beta are +rt3 and-rt3

new roots of the required equation

rt3+2 and -rt3+2

Sum of roots = rt3+2-rt3+2=4

product of roots= (rt3+2)(-rt3+2)

=4-3=1

Required equation is=> x^2-4x+1=0