Q. 23

# If f(x) = ax^{2} + bx + c is a quadratic polynomial such that f(0) = 0 and f(1) = 1. Prove that, f(x) = ax^{2} + (1 – a)x.

Answer :

**Explanation:**

f(x) = ax^{2} + bx + c

f(0) = a(0)^{2} + b. 0 + c

f(0) = c = 0

Therefore, c = 0

Now, f(x) = ax^{2} + bx

Also,

f(1) = 1

a(1)^{2} + b. 1 = 1

a + b = 1

b = (1 – a)

**f(x) = ax ^{2} + (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 Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

The zeroes of the polynomial p (x) = x^{2} + x - 6 are

Zero of the polynomial p(x) = 2x + 3 is

RS Aggarwal & V Aggarwal - MathematicsIf find

(i) f (0)

(ii) f (4)

(iii) f (-5)

RS Aggarwal & V Aggarwal - MathematicsIf 2 and -1/3 are the zeros of the polynomial 3x^{3} - 2x^{2} - 7x - 2 find the third zero of the polynomial.

If (x + 1) is a factor of 2x^{2}+ kx, then k =?

If (x^{2}+ kx – 3) = (x – 3 ) (x + 1) then k =?

The zeroes of the polynomial p (x) = x^{2} – 3x are

The zeroes of the polynomial p (x) = 3x^{2} – 1 are

If p(x) = x^{3} + x^{2} + ax + 115 is exactly divisible by (x + 5) then a = ?