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Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder?
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Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when div...
Solution:
Given:
Polynomial 1: \(ax^3 + 3x^2 - 13\)
Polynomial 2: \(2x^3 - 5x + a\)
When divided by x-2:
1. Let's first find the remainder when Polynomial 1 is divided by x-2:
- Using the Remainder Theorem, substitute x=2 in Polynomial 1:
\(a(2)^3 + 3(2)^2 - 13 = 8a + 12 - 13 = 8a - 1\)
2. Now, let's find the remainder when Polynomial 2 is divided by x-2:
- Using the Remainder Theorem, substitute x=2 in Polynomial 2:
\(2(2)^3 - 5(2) + a = 16 - 10 + a = 6 + a\)
Since the remainders are the same:
3. Equate the remainders:
\(8a - 1 = 6 + a\)
\(8a - a = 6 + 1\)
\(7a = 7\)
\(a = 1\)
Therefore, the value of \(a\) is 1.
Given:
Polynomial 1: \(ax^3 + 3x^2 - 13\)
Polynomial 2: \(2x^3 - 5x + a\)
When divided by x-2:
1. Let's first find the remainder when Polynomial 1 is divided by x-2:
- Using the Remainder Theorem, substitute x=2 in Polynomial 1:
\(a(2)^3 + 3(2)^2 - 13 = 8a + 12 - 13 = 8a - 1\)
2. Now, let's find the remainder when Polynomial 2 is divided by x-2:
- Using the Remainder Theorem, substitute x=2 in Polynomial 2:
\(2(2)^3 - 5(2) + a = 16 - 10 + a = 6 + a\)
Since the remainders are the same:
3. Equate the remainders:
\(8a - 1 = 6 + a\)
\(8a - a = 6 + 1\)
\(7a = 7\)
\(a = 1\)
Therefore, the value of \(a\) is 1.
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Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder?
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Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder? 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 Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder?.
Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder? 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 Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if the polynomial ax³+3x²-13 and 2x³-5x+a when divided by x-2 leaves the same remainder?.
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