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:

JEE Main 2017 Mathematics question

Let be a quadratic polynomial such that . If leaves remainder when divided by and it leaves remainder when divided by then:

Answer: (1)

Write . By the remainder theorem the remainder on division by is , so the three conditions read

p(0) = c = 1, p(1) = a+b+c = 4, p(-1) = a-b+c = 6.

From the last two, and . Adding gives , so and . Hence

p(x) = - x +

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Question ID VK-115824