Question

What is a equation that has a zero of -2 with a multiplicity of 3, a zero of 1 with a multiplicity of 1, degree of 4, and rises to the right and rises to the left

Answer 1

x^4+8x^3+18x-27=0

Explanation:

In a equation of the form

`(x-a)^n(x-b)^m=0`

you have roots in x=a and x=b, and multiplicity of n and m respectively.

Hence, the equation is

`(x-(-2))^3(x-1)=0\\(x+2)^3(x-1)=0\\`

by expanding the factors you have

`(x^3+3x^2(3)+3x(3)^2+(3)^3)(x-1)=0\\(x^3+9x^2+27x+27)(x-1)=0\\x^4+9x^3+27x^2+27x-x^3-9x^2-27x-27=0\\x^4+8x^3+18x^2-27=0`

HOPE THIS HELPS!!