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)?

Question

shaniehh · Answer

–2
–3
3
36

shaniehh · Answer

@dan815 @zepdrix

shaniehh · Answer

@Whitemonsterbunny17 @pooja195 @triciaal @jigglypuff314 @Jaynator495

shaniehh · Answer

@Directrix

campbell_st · Answer

so the polynomial is 

$$P(x) = a(x + b)^2(x-c)$$

is that correct...?

campbell_st · Answer

so the polynomial has factors 

$$(x + b)^2 $$

this has multiplicity or 2 and has a zero at x + b = 0   or x = -b

then linear factor is x - c = 0   so a zero exists at x = c

compare this to the given information 

multiplicity 2 at (-3, 0)  so x =-3   compare this to the zero above with multiplicty 2

x = -b

then you can say b = 3

so the same for x = c   you a told of a zero at (2, 0)   or x = 2

so c = 2

so the polynomial is 

$$P(x) = a(x+ 3)^2(x - 2)$$

now to find a, use the point (0,36) substitute x = 0 and P(x) = 36 then solvee for a

hope it helps

shaniehh · Answer

so the answer is D @campbell_st