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If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference is
- a)± 1
- b)± 2
- c)± 3
- d)± 4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their commo...
Factorize the equation and we get ( x - 1 ) ( x - 4 ) ( x - 7 )
Explanation:
Given Equation: x³ - 12x² + 39x - 28 = 0
Roots in an AP:
Let the roots of the equation be a - d, a, a + d, where d is the common difference.
Sum of roots: = -b/a
Sum of roots = a - d + a + a + d = 3a
From the equation, we know that sum of roots = -(-12) = 12
Therefore, 3a = 12
a = 4
Product of roots: = -d/a
Product of roots = (a - d)(a)(a + d) = 4(a2 - d2) = 28
Substitute a = 4 in the equation:
42 - d² = 7
16 - d² = 7
d² = 9
d = ±3
Therefore, the correct answer is C: ±3.
Explanation:
Given Equation: x³ - 12x² + 39x - 28 = 0
Roots in an AP:
Let the roots of the equation be a - d, a, a + d, where d is the common difference.
Sum of roots: = -b/a
Sum of roots = a - d + a + a + d = 3a
From the equation, we know that sum of roots = -(-12) = 12
Therefore, 3a = 12
a = 4
Product of roots: = -d/a
Product of roots = (a - d)(a)(a + d) = 4(a2 - d2) = 28
Substitute a = 4 in the equation:
42 - d² = 7
16 - d² = 7
d² = 9
d = ±3
Therefore, the correct answer is C: ±3.
Most Upvoted Answer
If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their commo...
To find the common difference in an arithmetic progression (AP), we need to find the difference between consecutive terms.
Let's assume that the roots of the given equation are a - d, a, and a + d, where a is the middle term and d is the common difference.
By Vieta's formulas, we know that the sum of the roots of a cubic equation is equal to the coefficient of the quadratic term divided by the coefficient of the cubic term. In this case, the sum of the roots is 12/1 = 12.
Since the roots are in an AP, we can write the sum of the roots as (a - d) + a + (a + d) = 12.
Simplifying this equation, we get 3a = 12, so a = 4.
Thus, the roots of the equation are 4 - d, 4, and 4 + d.
To find the common difference, we can subtract consecutive terms:
(4 + d) - 4 = d.
Therefore, the common difference is d = 4.
So, the common difference in this arithmetic progression is 4.
Let's assume that the roots of the given equation are a - d, a, and a + d, where a is the middle term and d is the common difference.
By Vieta's formulas, we know that the sum of the roots of a cubic equation is equal to the coefficient of the quadratic term divided by the coefficient of the cubic term. In this case, the sum of the roots is 12/1 = 12.
Since the roots are in an AP, we can write the sum of the roots as (a - d) + a + (a + d) = 12.
Simplifying this equation, we get 3a = 12, so a = 4.
Thus, the roots of the equation are 4 - d, 4, and 4 + d.
To find the common difference, we can subtract consecutive terms:
(4 + d) - 4 = d.
Therefore, the common difference is d = 4.
So, the common difference in this arithmetic progression is 4.
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If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer?
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If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer?.
If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of x3 - 12x2 + 39x - 28 = 0 are in an AP then their common difference isa)± 1b)± 2c)± 3d)± 4Correct answer is option 'C'. Can you explain this answer?.
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