How do you write a polynomial equation of least degree given the roots -1, 1, 3, -3?

1 Answer
Aug 11, 2018

x^4-10x^2+9 = 0x410x2+9=0

Explanation:

A polynomial in xx has a zero aa if and only if it has a factor (x-a)(xa).

So a polynomial in xx with zeros -11, 11, 33 and -33 must be a multiple of:

(x+1)(x-1)(x-3)(x+3) = (x^2-1)(x^2-9) = x^4-10x^2+9(x+1)(x1)(x3)(x+3)=(x21)(x29)=x410x2+9

So a polynomial equation of minimum degree with roots -11, 11, 33 and -33 is:

x^4-10x^2+9 = 0x410x2+9=0