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

1 Answer
Aug 11, 2018

Answer:

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

Explanation:

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

So a polynomial in #x# with zeros #-1#, #1#, #3# and #-3# must be a multiple of:

#(x+1)(x-1)(x-3)(x+3) = (x^2-1)(x^2-9) = x^4-10x^2+9#

So a polynomial equation of minimum degree with roots #-1#, #1#, #3# and #-3# is:

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