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Find the value of a such that x minus 5 a factor of x cube minus 3 X square a x - 10?
Most Upvoted Answer
Find the value of a such that x minus 5 a factor of x cube minus 3 X s...
Given:
We are given that x - 5 is a factor of x^3 - 3x^2 + ax - 10.
To Find:
We need to find the value of 'a' for which x - 5 is a factor of the given polynomial.
Explanation:
To find the value of 'a', we need to use the factor theorem. According to the factor theorem, if x - c is a factor of a polynomial f(x), then f(c) = 0.
In this case, x - 5 is a factor of x^3 - 3x^2 + ax - 10. So, when we substitute x = 5 into the polynomial, the result should be zero.
Substituting x = 5 into the polynomial, we get:
(5)^3 - 3(5)^2 + a(5) - 10 = 0
Simplifying the equation, we have:
125 - 75 + 5a - 10 = 0
50 + 5a = 10
5a = 10 - 50
5a = -40
a = -40/5
a = -8
Therefore, the value of 'a' for which x - 5 is a factor of x^3 - 3x^2 + ax - 10 is -8.
Summary:
The value of 'a' for which x - 5 is a factor of x^3 - 3x^2 + ax - 10 is -8.
We are given that x - 5 is a factor of x^3 - 3x^2 + ax - 10.
To Find:
We need to find the value of 'a' for which x - 5 is a factor of the given polynomial.
Explanation:
To find the value of 'a', we need to use the factor theorem. According to the factor theorem, if x - c is a factor of a polynomial f(x), then f(c) = 0.
In this case, x - 5 is a factor of x^3 - 3x^2 + ax - 10. So, when we substitute x = 5 into the polynomial, the result should be zero.
Substituting x = 5 into the polynomial, we get:
(5)^3 - 3(5)^2 + a(5) - 10 = 0
Simplifying the equation, we have:
125 - 75 + 5a - 10 = 0
50 + 5a = 10
5a = 10 - 50
5a = -40
a = -40/5
a = -8
Therefore, the value of 'a' for which x - 5 is a factor of x^3 - 3x^2 + ax - 10 is -8.
Summary:
The value of 'a' for which x - 5 is a factor of x^3 - 3x^2 + ax - 10 is -8.
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Find the value of a such that x minus 5 a factor of x cube minus 3 X square a x - 10?
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Find the value of a such that x minus 5 a factor of x cube minus 3 X square a x - 10? 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 such that x minus 5 a factor of x cube minus 3 X square a x - 10? 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 such that x minus 5 a factor of x cube minus 3 X square a x - 10?.
Find the value of a such that x minus 5 a factor of x cube minus 3 X square a x - 10? 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 such that x minus 5 a factor of x cube minus 3 X square a x - 10? 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 such that x minus 5 a factor of x cube minus 3 X square a x - 10?.
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