Let p x be a quadratic polynomial such that p 0 = 1 . If p x leaves remainder 4 when divided by x - 1 and it leaves remainder 6 when divided by x + 1 then:

Step-by-step solution

Assume , p x = a x 2 + b x + c Given , p 0 = 1 ⇒ c = 1 Now, p 1 = 4 p - 1 = 6 a + b + c   = 4 a - b +   c = 6 ⇒ a + b + 1   = 4 a - b + 1 = 6   a + b   = 3 a - b = 5   ⇒       a = 4             b = - 1 p x = 4 x 2 - x + 1 p - 2 = 16 + 2 + 1 = 19