Q3 of 16 Page 150

Find polynomials p(x) satisfying each set of conditions below.

Second degree polynomial with p(0) = 0, p(1) = 2 and p(2) = 6.

Let the polynomial be p(x)

p(x) = ax2 + bx + c (a,b,c are constants)


⇒ p(0) = c = 0


⇒ p(1) = a + b = 2 – (1)(∵ c = 0)


⇒ p(2) = 4a + 2b = 6 – (2)


By (1) and (2)


a = 1, b = 1


⇒ p(x) = x2 + x


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