Question

if alpha and beta are zeroes of quad polynomial f(x) x^2-3x-2, find quad polynomial whose zeroes are (alpha+ beta)^2 and (alpha-beta)^2

Answer 1

Answer:

x² - 26x + 153

Step-by-step explanation:

x² - 3x - 2 = 0

Alpha , Beta =  {-(-3) +/- √((-3)²-4(1)(-2)) } / (2(1))

= {3 +/- √(17) }/2

Alpha + beta =  3

(alpha + beta)² = 9

Alpha - beta = +/- √(17)

(Alpha - Beta)² = 17

(x -9)(x-17) = 0

x² - 26x + 153 = 0

Polynomial = x² - 26x + 153