Question

If alpha and beta are zeroes of the polynomial 2x^2-3x+8 then find {[(alpha)^-2]+[(beta)^-2]}

Answer 1

★Heya★

GIVEN QUESTION IS :-

2x² - 3x + 8

Find ( Alfa )-² + ( Beta )-²

EXP:-

(Alfa + Beta) = 3/2

And

( Alfa × Beta ) = 8/2 = 4

Alfa² + Beta² = ( Alfa + Beta )² -2 Alfa × Beta

=>

(Alfa)-² + (Beta)-² =

{(Alfa)² + (Beta)²}/ {(Alfa)² + (Beta)² }

=>

{ (Alfa)-² + (Beta)-² } =

(3/2)² - 2 × ( 4 )
___________
16

=>

{(Alfa)-² + (Beta)-²} = -92