Question

What polynomial has roots of -5,-4 and 1

Answer 1

x³ + 8x² + 11x - 20 ← the first on list

given the roots of a polynomial, say x = a, x = b and x = c

then the factors are (x - a), (x - b) and (x - c)

the polynomial is the product of the factors

f(x) = (x - a)(x - b)(x - c)

here x = - 5, x = - 4 and x = 1, hence factors are

(x + 5), (x + 4) and (x - 1)

f(x) =(x + 5)(x + 4)(x - 1) ← expanding factors gives

f(x) = (x² + 9x + 20)(x - 1) = x³ + 8x² + 11x - 20