If , , and are zeroes of the polynomial equation x^4-3 x^2+6 x-12=0 , then the value of + + ^2 + + + ^2 + + + ^2 + + + ^2 is equal to

Step-by-step solution

Given equation x^4-3 x^2+6 x-12=0 ...(i) On comparing with a x^4+b x^3+c x^2+d x+e=0a=1, b=0, c=-3, d=6, e=-12 , , , are the zeroes of polynomial equation. + + + = -b a =0 + + =- , + + =- + + =- , + + =- gathered = c a =-3 = -d a =-6 = e a =-12 gathered Consider, + + ^2 + + + ^2 + + + ^2 + + + ^2 aligned & = - ^2 + - ^2 + - ^2 + - ^2 & =- 1 - 1 - 1 - 1 & =- ( + + + ) & =- ( )=- ( -6 -12 )= -1 2 aligned