How do you write a polynomial function of least degree that has real coefficients, the following given zeros -5,2,-2 and a leading coefficient of 1?

1 Answer
Jun 28, 2016

Answer:

The required polynomial is #P(x)=x^3+5x^2-4x-20#.

Explanation:

We know that: if #a# is a zero of a real polynomial in #x# (say), then #x-a# is the factor of the polynomial.

Let #P(x)# be the required polynomial.

Here #-5,2,-2# are the zeros of required polynomial.
#implies {x-(-5)},(x-2)# and #{x-(-2)}# are the factors of the required polynomial.
#implies P(x)=(x+5)(x-2)(x+2)=(x+5)(x^2-4)#
#implies P(x)=x^3+5x^2-4x-20#

Hence, the required polynomial is #P(x)=x^3+5x^2-4x-20#