How do you write a polynomial equation of least degree given the roots -1, 1, 5?
So a polynomial of minimum degree with zeros
#(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
#x^3-5x^2-x+5 = 0#
Any non-zero constant multiple of this cubic equation is also a soltuion.