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The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202?
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The equation 3x2 mx n = 0 has roots that are double that of the eq...
Solution:
Given that the roots of the equation 3x^2 - mx + n = 0 are double that of the equation x^2 - 10x + 12 = 0.
Let the roots of the equation x^2 - 10x + 12 = 0 be α and β.
Then, α + β = 10 and αβ = 12.
The roots of the equation 3x^2 - mx + n = 0 are double of α and β.
Therefore, the roots of the equation 3x^2 - mx + n = 0 are 2α and 2β.
Sum of roots of the equation 3x^2 - mx + n = 0 is given by - b/a.
Hence, 2α + 2β = - (-m)/3
=> α + β = - m/6
=> 10 = - m/6
=> m = -60
Product of roots of the equation 3x^2 - mx + n = 0 is given by c/a.
Hence, (2α)(2β) = n/3
=> 4αβ = n/3
=> 4(12) = n/3 (Substitute αβ = 12)
=> n = 144
Therefore, m + n = -60 + 144 = 84.
Hence, the value of m + n is 84.
Therefore, the correct option is (d) 202.
Hence, the value of m and n is 60 and 144 respectively.
Given that the roots of the equation 3x^2 - mx + n = 0 are double that of the equation x^2 - 10x + 12 = 0.
Let the roots of the equation x^2 - 10x + 12 = 0 be α and β.
Then, α + β = 10 and αβ = 12.
The roots of the equation 3x^2 - mx + n = 0 are double of α and β.
Therefore, the roots of the equation 3x^2 - mx + n = 0 are 2α and 2β.
Sum of roots of the equation 3x^2 - mx + n = 0 is given by - b/a.
Hence, 2α + 2β = - (-m)/3
=> α + β = - m/6
=> 10 = - m/6
=> m = -60
Product of roots of the equation 3x^2 - mx + n = 0 is given by c/a.
Hence, (2α)(2β) = n/3
=> 4αβ = n/3
=> 4(12) = n/3 (Substitute αβ = 12)
=> n = 144
Therefore, m + n = -60 + 144 = 84.
Hence, the value of m + n is 84.
Therefore, the correct option is (d) 202.
Hence, the value of m and n is 60 and 144 respectively.
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The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202?
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The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202? 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 The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202?.
The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202? 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 The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 3x2 mx n = 0 has roots that are double that of the equation x2 10x 12 = 0. What is the value of m n? (a) 104 (b) 204 (c) 102 (d) 202?.
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