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The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a?
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The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the ...
Given Information:
- Polynomials: ax³-3x²+4 and 2x³-5x+a
- Divisor: x-2
- Remainders: p and q
- Relationship between p and q: p-2q=4
Steps to Find the Value of 'a':
Step 1: Finding the Remainders
- When ax³-3x²+4 is divided by x-2, the remainder is p.
- When 2x³-5x+a is divided by x-2, the remainder is q.
Step 2: Finding the Remainders Algebraically
- Using the Remainder Theorem, substitute x=2 in the polynomials to find the remainders:
- For ax³-3x²+4: p = a(2)³ - 3(2)² + 4 = 8a - 12 + 4 = 8a - 8
- For 2x³-5x+a: q = 2(2)³ - 5(2) + a = 16 - 10 + a = 6 + a
Step 3: Solving the Relationship
- Given p-2q = 4, substitute the expressions for p and q:
- 8a - 8 - 2(6 + a) = 4
- 8a - 8 - 12 - 2a = 4
- 6a - 20 = 4
- 6a = 24
- a = 4
Conclusion:
- The value of 'a' is 4.
- Polynomials: ax³-3x²+4 and 2x³-5x+a
- Divisor: x-2
- Remainders: p and q
- Relationship between p and q: p-2q=4
Steps to Find the Value of 'a':
Step 1: Finding the Remainders
- When ax³-3x²+4 is divided by x-2, the remainder is p.
- When 2x³-5x+a is divided by x-2, the remainder is q.
Step 2: Finding the Remainders Algebraically
- Using the Remainder Theorem, substitute x=2 in the polynomials to find the remainders:
- For ax³-3x²+4: p = a(2)³ - 3(2)² + 4 = 8a - 12 + 4 = 8a - 8
- For 2x³-5x+a: q = 2(2)³ - 5(2) + a = 16 - 10 + a = 6 + a
Step 3: Solving the Relationship
- Given p-2q = 4, substitute the expressions for p and q:
- 8a - 8 - 2(6 + a) = 4
- 8a - 8 - 12 - 2a = 4
- 6a - 20 = 4
- 6a = 24
- a = 4
Conclusion:
- The value of 'a' is 4.
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The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a?
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The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a? 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 ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a?.
The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a? 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 ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polynomials ax³-3x²+4 and 2x³-5x+a when divided by x-2 leaves the reminder p and q respectively. If p-2q=4, find the value of a?.
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