Question

Fina a polynomial function of degree 3 with real coefficients that has -1,2,-4 as zeros

Answer 1

Answer:

f(x) = x³ + 3x² - 6x - 8

Step-by-step explanation:

given the zeros of a polynomial x = a, x = b, x = c then

(x - a), (x - b), (x - c) are the factors of the polynomial and f(x) is the product of the factors

here x = - 1, x = 2 and x = - 4 are the zeros, hence

(x + 1), (x - 2) and (x + 4) are the factors

f(x) = a(x + 1)(x - 2)(x + 4) ← a is a multiplier

let a = 1, then

f(x) = (x + 1)(x - 2)(x + 4)

     = (x² - x - 2)(x + 4)

     = x³ - x² - 2x + 4x² - 4x - 8

     = x³ + 3x² - 6x - 8