Question

What is the value of the leading coefficient a if the polynomial function P(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−3, 0) and also passes through the points (2, 0) and (0, 36)?

answers:
−2−3336

Answer 1

The polynomial is of the form:


`P(x)=a (x+b)^(2)(x-c)`

We are provided with the two zeros in the question statement. The zero with multiplicity 2 is -3, and zero with multiplicity 1 is 2. So using these values, the polynomial becomes:


`P(x)=a (x+3)^(2)(x-2)`

The polynomial also passes from the point (0,36). This mean if we substitute x=0, the answer should be 36.


`P(0)=36=a (0+3)^(2)(0-2) \\ \\ 36=a(9)(-2) \\ \\ 36=-18a \\ \\ a=-2`

Thus the value of a for given polynomial will be -2. The complete equation of polynomial will be:


`P(x)=-2 (x+3)^(2)(x-2)`