Let f(x)=a1x2+b1x+c1
and g(x)=a2x2+b2x+c2
where a1≠a2≠0
h(x) is also a quadratic polynomial as a1≠a2
Since, h(x)=0 only at x=−3,
x=−3 is a repeated root of h(x)=0.
Let h(x)=k(x+3)2, where k is a non-zero constant.
h(−1)=6⇒k(−1+3)2=6
⇒k=32
⇒h(x)=32(x+3)2
∴h(5)=32(5+3)2=96