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Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.?
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Find the zeros of the polynomial x cube - 15x square 71x -105 , give...
As the zeroes are in AP, let the zeroes be a-d, a, a+d.
The sum of zeroes of the given polynomial is -(-15)/1 = 15.
Therefore, a-d + a + a+d=15. Hence, a = 5.
Also, the product of zeroes is -(-105)/1 = 105.
Therefore, 5(5-d)(5+d)=105, or 25 - d^2 = 21.
Then, d^2 = 4. Hence, d=+-2.
Therefore, the zeroes are 3, 5, 7.
The sum of zeroes of the given polynomial is -(-15)/1 = 15.
Therefore, a-d + a + a+d=15. Hence, a = 5.
Also, the product of zeroes is -(-105)/1 = 105.
Therefore, 5(5-d)(5+d)=105, or 25 - d^2 = 21.
Then, d^2 = 4. Hence, d=+-2.
Therefore, the zeroes are 3, 5, 7.
Community Answer
Find the zeros of the polynomial x cube - 15x square 71x -105 , give...
Introduction:
In this problem, we are given a polynomial of degree 3 and we have to find its zeros which are in AP.
Method:
To find the zeros of the polynomial which are in AP, we will use the following steps:
1. Assume the zeros of the polynomial in AP to be a-d, a, a+d where d is the common difference.
2. Using the sum of roots formula, a-d+a+a+d = 15/1 which gives a=5.
3. Substituting the value of a in the polynomial, we get x^3 - 15x^2 + 71x - 105 = (x-5)(x^2 - 10x + 21)
4. The quadratic factor can be factored as (x-3)(x-7) which gives the zeros as 5, 3, and 7.
Conclusion:
The zeros of the given polynomial x^3 - 15x^2 + 71x - 105 in AP are 3, 5, and 7.
In this problem, we are given a polynomial of degree 3 and we have to find its zeros which are in AP.
Method:
To find the zeros of the polynomial which are in AP, we will use the following steps:
1. Assume the zeros of the polynomial in AP to be a-d, a, a+d where d is the common difference.
2. Using the sum of roots formula, a-d+a+a+d = 15/1 which gives a=5.
3. Substituting the value of a in the polynomial, we get x^3 - 15x^2 + 71x - 105 = (x-5)(x^2 - 10x + 21)
4. The quadratic factor can be factored as (x-3)(x-7) which gives the zeros as 5, 3, and 7.
Conclusion:
The zeros of the given polynomial x^3 - 15x^2 + 71x - 105 in AP are 3, 5, and 7.
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Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.?.
Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the zeros of the polynomial x cube - 15x square 71x -105 , given that the zeros are in A.P.?.
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