Question

- Given that a and b are the zeros of the

polynomial f(x)=x²-x-6 with a>b,
and that g(x)=f(x+2) find:
(a) g(a)+g(b)
(b) g(a)-g(b)
(c) g(a) g(b)

Answer 1

x² - x - 6 = 0

(x - 3)(x + 2) = 0

a = 3, b = -2

(a) g(3) + g(-2) = f(5) + f(0) = 14 + 6 = 20

(b) g(3) - g(-2) = f(5) - f(0) = 14 - 6 = 8

(c) g(3)g(-2) = f(5)f(0) = 14(6) = 84