Find a second degree polynomial p(x) such that p(1) = 0 and p(–2) = 0.

Given, p(1) = 0, p(– 2) = 0

Need to find a polynomial p(x) of second degree

⇒ since we know that p(1) = 0

∴ if x = 1 is substituted in p(x) then it satisfies the equation

⇒ x – 1 = 0 , and x – 1 is one factor of p(x)

And p(– 2) = 0 is given

⇒ if x = – 2 is substituted in p(x) then it satisfies the equation

⇒ x + 2 = 0, and x + 2 is one factor of p(x)

⇒ since, x – 1 and x + 2 are the factors of p(x), it can be written as follows

⇒ p(x) = (x – 1)(x + 2)

⇒ p(x) = x² – x + 2x – 2

⇒ p(x) = x² + x – 2

∴ x² + x – 2 is the second degree polynomial which satisfies p(1) = 0 and p(– 2) = 0.