Question

if alpha, beta re the zeros of the polynomial 2x2-4x+5 find the value of (i) alpha2 + beta2 (ii) (alpha-beta)2

Answer 1

2x² - 4x +5 =0
α+β = -(-4/2) = 2
αβ = 5/2
i)α² +β² = (α+β)² - 2αβ
             = (2)²- 2×(5/2) = 4-5 
             = -1
ii)(α-β)² = (α+β)² - 4αβ
             =(2)² - 4×(5/2) = 4 - 10
             = -6

Answer 2

(i) (alpha + beta)²= alpha² + 2(alpha)(beta) + beta²

(2)² = alpha² + 10/2 + beta²
4- 5= alpha² + beta²
-1= alpha² + beta²

(ii) (alpha - beta)² = alpha² - 2(alpha)(beta) + beta²
= -1 - 5 = -6