Q. 53.8( 70 Votes )

If f(x) = x4 – 2x2 + ax + b is divided by (x – 2), the remainder is 4. If (a + b) = –4. Find the value of a.

Answer :

Concept Used:


Remainder theorem: If a polynomial f(x) is divided by (x – a) then f(a) will give the remainder.


Explanation:


f(x) = x4 – 2x2 + ax + b


f(2) = (2)4 – 2(2)2 + a.2 + b


f(2) = 16 – 8 + 2a + b


f(2) = 8 + 2a + b


f(2) = 4


8 + 2a + b = 4


2a + b = –4


a + (a + b) = –4


a – 4 = –4


a = 0


Hence, the value of a is 0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Polynomials - Zero to HeroPolynomials - Zero to HeroPolynomials - Zero to Hero42 mins
Genius Quiz | PolynomialsGenius Quiz | PolynomialsGenius Quiz | Polynomials40 mins
Zeros and Degrees of a PolynomialZeros and Degrees of a PolynomialZeros and Degrees of a Polynomial41 mins
Champ Quiz | PolynomialsChamp Quiz | PolynomialsChamp Quiz | Polynomials29 mins
Genius Quiz |  Division of Algebraic ExpressionsGenius Quiz |  Division of Algebraic ExpressionsGenius Quiz | Division of Algebraic Expressions37 mins
Introduction to PolynomialsIntroduction to PolynomialsIntroduction to Polynomials37 mins
Quiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of PolynomialsBasic understanding of PolynomialsBasic understanding of Polynomials37 mins
Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-246 mins
Remainder Theorem and Factor TheoremRemainder Theorem and Factor TheoremRemainder Theorem and Factor Theorem38 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
caricature
view all courses