Class 9 Exam > Class 9 Questions > The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and ...
Start Learning for Free
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2?
Most Upvoted Answer
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 ...
**Finding the Value of a in Each Case**
**Given Polynomials:**
- \(x^3 + 2x^2 - 5ax - 7\)
- \(x^3 + ax^2 - 12x + 6\)
**Divisors:**
- \(x + 1\)
- \(x - 2\)
**Remainders:**
- Let the remainder when the first polynomial is divided by \(x + 1\) be \(R_1\)
- Let the remainder when the second polynomial is divided by \(x - 2\) be \(R_2\)
1. **Finding the Remainder \(R_1\):**
- Substitute \(-1\) for \(x\) in the first polynomial:
\(R_1 = (-1)^3 + 2(-1)^2 - 5a(-1) - 7\)
- Simplify the expression to find \(R_1\)
2. **Finding the Remainder \(R_2\):**
- Substitute \(2\) for \(x\) in the second polynomial:
\(R_2 = 2^3 + a(2)^2 - 12(2) + 6\)
- Simplify the expression to find \(R_2\)
3. **Setting the Remainders Equal:**
- Since the remainders are equal, we have:
\(R_1 = R_2\)
- Substitute the expressions for \(R_1\) and \(R_2\) found in steps 1 and 2
- Solve for \(a\) by equating the two expressions
4. **Calculating the Value of \(a\):**
- By solving the equation obtained in step 3, we can find the value of \(a\)
- This value of \(a\) will satisfy the condition that the remainders are equal
By following these steps and performing the necessary calculations, you can determine the value of \(a\) that satisfies the given conditions for both polynomials.
**Given Polynomials:**
- \(x^3 + 2x^2 - 5ax - 7\)
- \(x^3 + ax^2 - 12x + 6\)
**Divisors:**
- \(x + 1\)
- \(x - 2\)
**Remainders:**
- Let the remainder when the first polynomial is divided by \(x + 1\) be \(R_1\)
- Let the remainder when the second polynomial is divided by \(x - 2\) be \(R_2\)
1. **Finding the Remainder \(R_1\):**
- Substitute \(-1\) for \(x\) in the first polynomial:
\(R_1 = (-1)^3 + 2(-1)^2 - 5a(-1) - 7\)
- Simplify the expression to find \(R_1\)
2. **Finding the Remainder \(R_2\):**
- Substitute \(2\) for \(x\) in the second polynomial:
\(R_2 = 2^3 + a(2)^2 - 12(2) + 6\)
- Simplify the expression to find \(R_2\)
3. **Setting the Remainders Equal:**
- Since the remainders are equal, we have:
\(R_1 = R_2\)
- Substitute the expressions for \(R_1\) and \(R_2\) found in steps 1 and 2
- Solve for \(a\) by equating the two expressions
4. **Calculating the Value of \(a\):**
- By solving the equation obtained in step 3, we can find the value of \(a\)
- This value of \(a\) will satisfy the condition that the remainders are equal
By following these steps and performing the necessary calculations, you can determine the value of \(a\) that satisfies the given conditions for both polynomials.
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2?
Question Description
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2?.
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2?.
Solutions for The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? defined & explained in the simplest way possible. Besides giving the explanation of
The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2?, a detailed solution for The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? has been provided alongside types of The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? theory, EduRev gives you an
ample number of questions to practice The polynomials 𝑥 3 + 2𝑥 2 − 5𝑎𝑥 − 7 and 𝑥 3 + 𝑎𝑥 2 − 12𝑥 + 6 when divided by x + 1 and x – 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases: i. R1 = R2? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup