Answer:
[tex]p(x) = - 0.7(x - 3)^{2} (x + 2)[/tex]
Step-by-step explanation:
We have that the polynomial, has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2.
This means the factored form of the polynomial will be.
[tex]p(x) = a(x - 3)^{2} (x + 2)[/tex]
Also, it was given that, the y-intercept is y=-12.6.
This implies that:
[tex] - 12.6= a(0 - 3)^{2} (0 + 2)[/tex]
[tex]- 12.6= a(- 3)^{2} (2)[/tex]
[tex]- 12.6= 18a[/tex]
Divide both sides by 18;
[tex]a = \frac{ - 12.6}{18} [/tex]
[tex]a= - 0.7[/tex]
Therefore the polynomial is
[tex]p(x) = - 0.7(x - 3)^{2} (x + 2)[/tex]
