Question

Write a polynomial function of at least one degree that has ration coefficients, a leading coefficient of 1, and given zeros of 4,2,1

Answer 1

x³-7x²+14x - 8

Explanation:

Given the zeros of the polynomial function to be 4, 2 and 1. Hence the factors of the polynomial will be x - 4, x - 2 and x - 1. The polynomial function in x will be expressed as:

P(x) = (x-4)(x-2)(x-1)

P(x) = (x²-2x-4x+8)(x-1)

P(x) = (x²-6x+8)(x-1)

P(x) = x³-x²-6x²+6x+8x-8

P(x) = x³-7x²+14x - 8

Hence the required polynomial function is x³-7x²+14x - 8