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

1 Answer
Aug 11, 2018

Answer:

#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.