Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
180 views
in Algebra by (115k points)
closed by
If x - 1 and x + 3 are the two factors of x3 + ax + b, then remaining factor is
1. x + 2
2. x - 2
3. x - 3
4. x + 1

1 Answer

0 votes
by (113k points)
selected by
 
Best answer
Correct Answer - Option 2 : x - 2

Given:

Factor of the x3 + ax + b is,

(x - 1), and (x + 3)

Calculation:

Let,

(x - β) is the remaining factor of the given equation then,

⇒ (x - β)(x - 1)(x + 3) = x3 + ax + b

⇒ (x - β)[x2 + 2x - 3] = x3 + ax + b

⇒ x3 + 2x2 - 3x - βx2 - 2βx + 3β = x3 + ax + b

⇒ x3 + x2(2 - β) - x(3 + 2β) + 3β = x3 + ax + b

On comparing both side,

⇒ 2 - β = 0

β = 2

Hence, the remaining factor is (x - 2)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...