Answer:
Cubic polynomial function with zeros 3,3 and -3 is [tex]\mathbf{x^3-3x^2-9x+27=0}[/tex]
Step-by-step explanation:
We need to find a cubic polynomial function with zeros 3,3 and -3.
If zeros of polynomial are: 3,3,and -3
we can write:
x=3, x=3, x=-3
Or
We can write:
x-3=0, x-3=0, x+3=0
Now, we can write them as:
(x-3)(x-3)(x+3)=0
Multiplying the terms, we can find the polynomial:
[tex](x-3)(x-3)(x+3)=0\\(x(x-3)-3(x-3))(x+3)=0\\(x^2-3x-3x+9)(x+3)=0\\(x^2-6x+9)(x+3)=0\\x(x^2-6x+9)+3(x^2-6x+9)=0\\x^3-6x^2+9x+3x^2-18x+27=0\\x^3-6x^2+3x^2+9x-18x+27=0\\x^3-3x^2-9x+27=0[/tex]
So, cubic polynomial function with zeros 3,3 and -3 is [tex]\mathbf{x^3-3x^2-9x+27=0}[/tex]
