Answer:
[tex]P(x)=x^2+x-6[/tex]
Step-by-step explanation:
Quadratic Polynomial
Assume we have a polynomial factored as:
P(x)=a(x-m)(x-n)
Where m and n are the zeros of P(x).
Operating:
[tex]P(x)=a(x^2-(m+n)x+mn)[/tex]
Note the coefficient of x is the negative sum of the zeros and the independent term is the product of the zeros.
If we are given the zeros m=-3 and n=2, then:
[tex]P(x)=a(x^2-(-3+2)x+(-3)(2))[/tex]
[tex]P(x)=a(x^2+x-6)[/tex]
We can choose any value for a, for example, a=2:
[tex]P(x)=2x^2+2x-12[/tex]
For a=1:
[tex]P(x)=x^2+x-6[/tex]
