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
130 views
in Aptitude by (105k points)
closed by

A quadratic polynomial in x leaves remainder 4, 4, and 0 respectively. when divided by (x - 1), (x - 2) and x - 3

Find the quadratic polynomial:


1. -2x2 + 6x + 5
2. -2x2 + 6x
3. -2x2 + 6x - 5
4. -2x2 + 6x + 3

1 Answer

0 votes
by (111k points)
selected by
 
Best answer
Correct Answer - Option 2 : -2x2 + 6x

Given:

Polynomial is quadratic, and 

Remainder = 4, when divided by (x - 1),

Remainder = 4, when divided by (x - 2)

Remainder = 0, when divided by (x - 3)

Concept:

Remainder theorem:

If a polynomial P(x) is divided by (x - a), then the remainder of the polynomial will be P(a).

Calculation

Let quadratic polynomail is

P(x) = ax2 + bx + c

Given that when P(x) is divided by (x - 1), the remainder comes 4, so by using the reminder theorem

As, a = 1

⇒ P(1) = 4

⇒ a(1)2 + b(1) + c = 4

⇒ a + b + c = 4   

⇒ c = 4 - a - b       ---(1)

Simmilarly, for (x - 2),  a = 2

⇒ P(2) = 4

⇒ a(2)+ b(2) + c = 4

⇒ 4a + 2b + c = 4    

From equation first, 

4a + 2b + 4 - a - b = 4

⇒ 3a + b = 0 

⇒ b = - 3a         ---(2)

Simmilarly, for (x - 3),  a = 3

⇒ a(3)+ b(3) + c = 0

⇒ 9a + 3b + c = 0

⇒ 8a + 2b = -4

⇒ 4a + b = -2

⇒ 4a - 3a = -2       From equation  (2)

⇒ a = -2  

⇒ b = 6          From equation  (2)

⇒ c = 4 - (-2) - 6 = 0      From equation  (1)

Hence, required polynomial will be -2x2 + 6x.

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.

Categories

...