Question

Write the simplest polynomial function with the given roots 1/2,5, and -2

Answer 1

x³-7x²/2-39x/2 + 10

Explanation:

Given 1/2,5, and -2 as roots of the polynomial, the function in terms of x is expressed as;

P(x) = (x - 1/2)(x - 5)(x+2)

Expand;

(x - 1/2)(x - 5) = x²-5x -x/2 + 5/2

(x - 1/2)(x - 5) = x²-11x/2 + 5/2

P(x) = (x²-11x/2 + 5/2)(x+2) = x³+2x²-11x²/2-22x+5x/2 + 10

P(x) = x³-7x²/2-39x/2 + 10

Hence the required polynomial is x³-7x²/2-39x/2 + 10