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If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,find the value of a ?
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If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remaind...
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If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remaind...
Explanation:
Given Information:
- Polynomials: 2x^3 + ax^2 + 3x - 5 and x^3 + x^2 - 4x + 5
- Both polynomials leave the same remainder when divided by x - 2
Using Remainder Theorem:
- When a polynomial f(x) is divided by x - a, the remainder is f(a)
- Let's denote the remainder for both polynomials as R
Calculating Remainder for the first polynomial:
- Substitute x = 2 in the first polynomial: R = 2^3 + a(2)^2 + 3(2) - 5
- R = 8 + 4a + 6 - 5 = 4a + 9
Calculating Remainder for the second polynomial:
- Substitute x = 2 in the second polynomial: R = 2^3 + 2^2 - 4(2) + 5
- R = 8 + 4 - 8 + 5 = 9
Equating the Remainders:
- Since both polynomials leave the same remainder when divided by x - 2, we have: 4a + 9 = 9
- Solving the equation: 4a = 0 => a = 0
Conclusion:
- The value of a is 0, which makes the first polynomial 2x^3 + 3x - 5.
Given Information:
- Polynomials: 2x^3 + ax^2 + 3x - 5 and x^3 + x^2 - 4x + 5
- Both polynomials leave the same remainder when divided by x - 2
Using Remainder Theorem:
- When a polynomial f(x) is divided by x - a, the remainder is f(a)
- Let's denote the remainder for both polynomials as R
Calculating Remainder for the first polynomial:
- Substitute x = 2 in the first polynomial: R = 2^3 + a(2)^2 + 3(2) - 5
- R = 8 + 4a + 6 - 5 = 4a + 9
Calculating Remainder for the second polynomial:
- Substitute x = 2 in the second polynomial: R = 2^3 + 2^2 - 4(2) + 5
- R = 8 + 4 - 8 + 5 = 9
Equating the Remainders:
- Since both polynomials leave the same remainder when divided by x - 2, we have: 4a + 9 = 9
- Solving the equation: 4a = 0 => a = 0
Conclusion:
- The value of a is 0, which makes the first polynomial 2x^3 + 3x - 5.
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If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,find the value of a ?
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If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,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 If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,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 If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,find the value of a ?.
If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,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 If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,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 If polynomials 2x^3 ax^2 3x-5 and x^3 x^2-4x 5 leaves the same remainder when divided by x-2 ,find the value of a ?.
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