Q. 205.0( 1 Vote )

If p (x) = 2x3 + ax2 + 3x – 5 and q (x) = x3 + x2 – 4x + a leave the same remainder when divided by (x – 2), show that

Answer :

We have,

p (x) = 2x3 + ax2 + 3x – 5


q (x) = x3 + x2 – 4x + a


It is given in the question that, when p (x) and q (x) is divided by (x – 2) it leaves same remainder


p (2) = q (2)


2 (2)3 + a (2)2 + 3 (2) – 5 = (2)3 + (2)2 – 4 (2) + a


2 × 8 + a × 4 + 3 × 2 – 5 = 8 + 4 – 4 × 2 + a


16 + 4a + 6 – 5 = 12 – 8 + a


16 + 4a + 1 = 4 + a


4a – a = 4 – 17


3a = - 13


a =


Hence proved


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
Introduction to Polynomials37 mins
Quiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of Polynomials37 mins
Genius Quiz | Division of Algebraic Expressions37 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