Question

Find the third degree polynomial function that has an output of 40 when x = 1, and has zeros - 19 and -i?

Answer 1

f(x) = x³ + 19x² + x + 19

Explanation:

Zeros: -19 , -i, complex conjugate root: +i

Function: (x+19)(x+i)(x-i) = 0

(x + 19) (x² - i²) = (x + 19) ( x² + 1) = x³ + 19x² + x + 19

check: when x = 1

f(1) = 1 + 19 + 1 +19 = 40