Question

Write a polynomial function of least degree with integral coefficients that has the given zeros. 4, -6, 1

Answer 1

Answer: f(x) = x³ + x² - 26x + 24

Step-by-step explanation:

x = 4             x = -6              x = 1

x - 4 = 0        x + 6 = 0         x - 1 = 0

(x - 4) (x + 6) (x - 1) = 0

(x² + 2x - 24)(x - 1) = 0

x(x² + 2x - 24)  -1(x² + 2x - 24) = 0

x³ + 2x² - 24x  -x² - 2x + 24  = 0

x³ + x² - 26x + 24 = 0