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The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ?
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The equation 3x^2 mx n=0 has roots that are double that of equation x...
Solution:
Given, the equation 3x^2 + mx + n = 0 has roots that are double that of equation x^2 + 10x + 12 = 0.
Let the roots of 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 that of α and β.
Let the roots of equation 3x^2 + mx + n = 0 be 2α and 2β.
Then, 2α + 2β = -m/3 and 4αβ = n/3.
We know that α + β = -10 and αβ = 12.
Substituting the values in the above equations, we get:
2(-10) = -m/3 => m = 60
4(12) = n/3 => n = 48
Therefore, the value of m is 60 and the value of n is 48.
Hence, the solution.
Given, the equation 3x^2 + mx + n = 0 has roots that are double that of equation x^2 + 10x + 12 = 0.
Let the roots of 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 that of α and β.
Let the roots of equation 3x^2 + mx + n = 0 be 2α and 2β.
Then, 2α + 2β = -m/3 and 4αβ = n/3.
We know that α + β = -10 and αβ = 12.
Substituting the values in the above equations, we get:
2(-10) = -m/3 => m = 60
4(12) = n/3 => n = 48
Therefore, the value of m is 60 and the value of n is 48.
Hence, the solution.
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The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ?
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The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ? 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 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ?.
The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ? 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 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation 3x^2 mx n=0 has roots that are double that of equation x^2 10x 12=0 . what is the value of m n ?.
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