If the polynomial function [tex]P(x) = a(x + b)^2(x-c) [/tex] has a multiplicity of 2 at the point (−1, 0) then the factor (x-(-1))=(x+1) twice enters the polynomial representation. So, you have known one part of the left side of the polynomial function that is [tex]P(x) = a(x + 1)^2(x-c) [/tex].
If polynomial function passes through the point (7,0), then [tex]0 = a(7+ 1)^2(7-c) [/tex] and since [tex]a\neq 0[/tex] you have that c=7.
At last, if polynomial function passes through the point (0,-14), then [tex]-14 = a(0+ 1)^2(0-7) [/tex] and [tex]-14=-7a[/tex], so a=2.
Answer: a=2.
