Question

There is a polynomial P(x) = ax3 + bx2 + cx + d such that P(0) = P(1) = – 2, P'(0) = –1, then find the value of a + b + c + d + 10.

Answer 1

Given P(x) = ax3 + bx2 + cx + d

P'(x) = 2ax2 + 2bx + c

P"(x) = 4ax + 2b

P"(0) = 10 ⇒ 2b = 10 ⇒b = 5

P(0) = – 2 ⇒ d = – 2

P(1) = – 2 ⇒ a + b + c + d = –2

a + 5 + c – 2 = –2

a + c = –5 ...(i)

P'(0) = – 1 ⇒ c –1

From (i), we get, a = – 4

Hence, the value of (a + b + c + d + 10)

= – 4 + 5 –1 –2 + 10

= 8