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)?

–2
–3
3
36

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)?

 –2
 –3
 3
 36

dumbcow · Answer

"multiplicity of 2" refers to the squared factor. x = -3  ---> x+3 = 0 ---> b = 3

the other root is x=2   ---> x-2=0  ---> c=2

Function contains point (0,36)

36 = a(0+3)^2(0-2)
solve for a

kittiwitti1 · Answer

Hmm... are you getting what @dumbcow said? o:

kittiwitti1 · Answer

multiplicity is like "root x=0 with multiplicity 3" would be x^3

princesssleelee · Answer

a=-2

kittiwitti1 · Answer

alright then, good job • D •)/