A polynomial function function is defined by the equation p(x)=3x3+ax2+bx+7, where a, bE/. If p(-2)=5 and p(1)=14 then the value of a+b is...

Answer 1

From p(-2)=5 and p(1)=14
we have two points (-2,5) and (1,14)

so,
3(-8) + a(4) -2b + 7 = 5
4a - 2b = 22 ----> 2a - b = 11

3(1) + a(1) + b(1) + 7 = 14 ---> a + b = 4

adding:
3a = 15
a = 5, then b = -1

a+b = 5-1 = 4