Question

If α and β are the zeroes of a quadratic polynomial x²+x-2 then find the value of (α/β+2) (β/α+2)

Answer 1

0

Explanation:

x²+x-2=0

(x-1)*(x+2)=0

x can be 1 or -2

when we put 1 and -2 for α and β we get 0

(-1/2+2)*(-2+2)=0

Answer 2

βα = -2 and α+β= -1

(α/β +2)(β/α+ 2)
= 1 + 4 + 2β/α + 2α/β
= 5 + 2(β/α+α/β)
= 5 + 2 [(α^2+β^2) / αβ]
α^2+β^2 = (α+β)^2 - 2αβ = 1 - 2(-2) = 5

SO THE ANSWER IS 5+2(5/-2) = 5 - 5 = 0