Question

Write a polynomial function of least degree with integral coefficients that have the given zeros. 4,-1,6 f(x)=x^3-9x^2+14x+24

Answer 1

see explanation

Explanation:

Given the zeros of a polynomial, say x = a, x = b, x = c

Then (x - a), (x - b), (x - c) are it's factors

and the polynomial is the product of the factors

here x = 4, x = - 1, x = 6, hence

(x - 4), (x + 1) and (x - 6) are the factors

f(x) = a(x - 4)(x + 1)(x - 6) ← a is a multiplier

let a = 1, then expanding the first pair of factors

f(x) = (x² - 3x - 4)(x - 6) ← expand out the factors

= x³ - 3x² - 4x - 6x² + 18x + 24 ← collect like terms

= x³ - 9x² + 14x + 24