Question

if alpha and beta are the zeros of the quadratic polynomial x2-2+x then (1/alpha+1/beta)^2

Answer 1

if alpha and beta are the zeros of the quadratic polynomial x2-2+x then (1/alpha+1/beta)^2

Answer 2

Answer:

Solution

α+β=−1andαβ=−2.

(β+α)2−(β−α)2=4αβ

⇒(β−α)2=(α+β)2−4αβ=(−1)2−4×(−2)=9

⇒β−α=3.

∴ (1/α−1/β)

= (β−α)/αβ

= 3/−2

= −3/2.