Q23 of 32 Page 2

If f(x) = ax2 + bx + c is a quadratic polynomial such that f(0) = 0 and f(1) = 1. Prove that, f(x) = ax2 + (1 – a)x.

Explanation:


f(x) = ax2 + bx + c


f(0) = a(0)2 + b. 0 + c


f(0) = c = 0


Therefore, c = 0


Now, f(x) = ax2 + bx


Also,


f(1) = 1


a(1)2 + b. 1 = 1


a + b = 1


b = (1 – a)


f(x) = ax2 + (1 – a)x.


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