Question

if alpha and beta are roots of the equation 3x^2-2x-8=0 then alpha^2-alpha beta+beta^2=?

Answer 1

using factor of 2x
3x^2-6x+4x-8=0
3x(x-2)+4(x-2)=0
(x-2)(3x+4)=0
x=2, x=-4/3
using this value in equation
alpha^-alpha beta +beta^2
alpha = 2,beta=-4/3
(2)^2-2*(-4/3)+(-4/3)^2
4+8/3+16/3
taking LCM
(36+24+16)/9=76/9
then again using alpha=(-4/3) and beta =2