How do you write a polynomial function given the real zeroes -2, -1, 0, 1, and 2 and coefficient 1?

1 Answer
Jan 2, 2016

Answer:

#f(x) = x^5-5x^3+4x#

Explanation:

#f(x) = (x+2)(x+1)x(x-1)(x-2)#

#=(x^2-4)(x^2-1)x#

#=(x^4-5x^2+4)x#

#=x^5-5x^3+4x#

This is the simplest polynomial in #x# with the required zeros.

Any other polynomial in #x# with these zeros is a multiple (scalar or polynomial) of this #f(x)#.

The polynomial graphed:

graph{x^5-5x^3+4x [-10, 10, -5, 5]}