Q. 23

# 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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Champ Quiz | Polynomials29 mins  Methods to find zeroes of a Polynomial-246 mins  Remainder Theorem and Factor Theorem38 mins  Polynomials - Zero to Hero42 mins  Genius Quiz | Polynomials40 mins  Zeros and Degrees of a Polynomial41 mins  Genius Quiz | Division of Algebraic Expressions37 mins  Introduction to Polynomials37 mins  Quiz | Imp. Qs. on Algebraic Identities65 mins  Basic understanding of Polynomials37 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 