Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2. The y-intercept is y=-12.6

Answer 1

Answer:

$p(x) = - 0.7(x - 3)^{2} (x + 2)$

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.

$p(x) = a(x - 3)^{2} (x + 2)$

Also, it was given that, the y-intercept is y=-12.6.

This implies that:

$- 12.6= a(0 - 3)^{2} (0 + 2)$

$- 12.6= a(- 3)^{2} (2)$

$- 12.6= 18a$

Divide both sides by 18;

$a = \frac{ - 12.6}{18}$

$a= - 0.7$

Therefore the polynomial is

$p(x) = - 0.7(x - 3)^{2} (x + 2)$