Question

50 POINTS PLS HELP ME I'LL MARK BRAINLIEST

Find a polynomial of degree n that has only the given zeros. (There are many correct answers.)


x = −3, 8; n = 3



Thank you so much!!

Answer 1

Answer:

Step-by-step explanation:

Here we need to find a 3rd degree polynomial that has only two distinct zeros:  {-3, 8}.  

Focusing on the zero x = 8 and assuming that this 8 has a multiplicity of 2, we come up with the following polynomial in which the factor x - 8 shows up twice:

f(x) = a(x - 8)(x - 8)(x + 3), or f(x) = a(x - 8)^2(x + 3)

One such polynomial is thus

f(x) = a(x - 8)^2(x + 3), where 'a' is a constant coefficient.  This polynomial has a double zero at x = 8 and a third zero at x = -3.

Answer 2

Step-by-step explanation:

The polynomial has degree 3 and two zeros: - 3 and 8.

Since it has degree 3 it should have 3 zero's.

Two possible scenarios

1. -3 has multiplicity of two:

• a(x + 3)²(x - 8) - is the factored form of the polynomial where a is the constant

2. 8 has multiplicity of two:

• a(x + 3)(x - 8)² - is the factored form of the polynomial