How do you write a polynomial with zeros -6, 3, 5 and leading coefficient 1?

1 Answer
Jan 21, 2018

x^3-2x^2-33x+90

Explanation:

This has 3 roots, so it will be a polynomial of degree 3. If we factor a 3rd degree polynomial we get:

(x+a)(x+b)(x+c) where a , b and c are constants:

We can find these constants using the known roots. If the roots are:

alpha=-6

beta=3

gamma=5

Since the constant term in each factor will have an opposite sign to the root, we have:

(x-alpha)(x-beta)(x-gamma)

Substituting alpha , beta and gamma for root values we have:

(x-(-6))(x-(3))(x-(5))=(x+6)(x-3)(x-5)

The coefficient of the first term is the product of the coefficients of the x terms in each factor, since these are all 1, the coefficient of the first term will be 1

(x+6)(x-3)(x-5)=x^3-2x^2-33x+90