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Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is?
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Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are...
Solution:
Ratio of roots: 3:2
Let the roots be 3a and 2a.
Sum of roots = -b/a = -K/12
3a+2a= -K/12
5a= -K/12
a = -(K/60)
Product of roots = c/a = 5/12K
(3a)(2a) = 5/12K
6a^2 = 5/12K
6[(-K/60)^2] = 5/12K
K^3/10000 = K/1440
K^2 = 14400000
K = + 4000 or - 3600
As K needs to be positive, the value of K is 4000.
Therefore, the positive value of 'K' for which the roots of the equation 12x^2 Kx 5=0 are in the ratio 3:2 is 4000.
Ratio of roots: 3:2
Let the roots be 3a and 2a.
Sum of roots = -b/a = -K/12
3a+2a= -K/12
5a= -K/12
a = -(K/60)
Product of roots = c/a = 5/12K
(3a)(2a) = 5/12K
6a^2 = 5/12K
6[(-K/60)^2] = 5/12K
K^3/10000 = K/1440
K^2 = 14400000
K = + 4000 or - 3600
As K needs to be positive, the value of K is 4000.
Therefore, the positive value of 'K' for which the roots of the equation 12x^2 Kx 5=0 are in the ratio 3:2 is 4000.
Summary:
Given equation: 12x^2 Kx 5=0
Ratio of roots: 3:2
Let the roots be 3a and 2a.
Sum of roots = -K/12
Product of roots = 5/12K
On solving the above equations, K = + 4000 or - 3600
As K needs to be positive, the value of K is 4000.
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Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is?
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Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is?.
Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Positive value of ‘K’ for which the roots at equation 12x^2 Kx 5=0 are in ratio 3:2 is?.
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