How do you write a polynomial equation of least degree given the roots -1, 1, 5?

1 Answer
Aug 11, 2018

x^3-5x^2-x+5 = 0

Explanation:

If a is a zero of a polynomial in x, then (x-a) is a factor and vice versa.

So a polynomial of minimum degree with zeros -1, 1 and 5 is:

(x+1)(x-1)(x-5) = (x^2-1)(x-5) = x^3-5x^2-x+5

and a polynomial equation of minimum degree with roots -1, 1 and 5 is:

x^3-5x^2-x+5 = 0

Any non-zero constant multiple of this cubic equation is also a soltuion.