What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)?

A.2
B.−2
C.7
D.−14

Question

What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)?

A.2
B.−2
C.7
D.−14

campbell_st · Answer

you have zeros at (-1, 0) and (7, 0)

so then you know   x = -1 as a zero then x + 1 is a factor multiplicity 2

and x = 7 as a factor is x - 7

so the polynomial is 

$$P(x) = a(x + 1)^2 (x -7) $$

now use the 3rd point 

(0, 14)   so P(x) = 14 when x = 0

substitute these values to find a

hope it makes sense

anonymous · Answer

it does thank you