Question

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

Answer 1

`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.