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Find the value of a if the polynomial ax³+3x²-13 and 2x²-5x+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 2x²-5x+a when div...
Given Information:
Given polynomials:
1. $ax^3 + 3x^2 - 13$
2. $2x^2 - 5x + a$
Condition:
When both polynomials are divided by $x-2$, they leave the same remainder.
Calculating Remainders:
When a polynomial $f(x)$ is divided by $x-c$, the remainder is $f(c)$.
1. Remainder of $ax^3 + 3x^2 - 13$ when divided by $x-2$ is $a(2)^3 + 3(2)^2 - 13 = 8a + 12 - 13 = 8a - 1$
2. Remainder of $2x^2 - 5x + a$ when divided by $x-2$ is $2(2)^2 - 5(2) + a = 8 - 10 + a = a - 2$
Since both polynomials leave the same remainder when divided by $x-2$, we can equate the remainders:
$8a - 1 = a - 2$
Solving the equation:
$8a - 1 = a - 2$
$7a = -1$
$a = -\frac{1}{7}$
Therefore, the value of $a$ is $-\frac{1}{7}$.
Given polynomials:
1. $ax^3 + 3x^2 - 13$
2. $2x^2 - 5x + a$
Condition:
When both polynomials are divided by $x-2$, they leave the same remainder.
Calculating Remainders:
When a polynomial $f(x)$ is divided by $x-c$, the remainder is $f(c)$.
1. Remainder of $ax^3 + 3x^2 - 13$ when divided by $x-2$ is $a(2)^3 + 3(2)^2 - 13 = 8a + 12 - 13 = 8a - 1$
2. Remainder of $2x^2 - 5x + a$ when divided by $x-2$ is $2(2)^2 - 5(2) + a = 8 - 10 + a = a - 2$
Since both polynomials leave the same remainder when divided by $x-2$, we can equate the remainders:
$8a - 1 = a - 2$
Solving the equation:
$8a - 1 = a - 2$
$7a = -1$
$a = -\frac{1}{7}$
Therefore, the value of $a$ is $-\frac{1}{7}$.
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Find the value of a if the polynomial ax³+3x²-13 and 2x²-5x+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 2x²-5x+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 2x²-5x+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 2x²-5x+a when divided by x-2 leaves the same remainder?.
Find the value of a if the polynomial ax³+3x²-13 and 2x²-5x+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 2x²-5x+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 2x²-5x+a when divided by x-2 leaves the same remainder?.
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