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The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2?
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The two roots of an equation X square - 6 X square + 14 x + 24 is equa...
Roots of the Equation in a Ratio of 3:2
The given equation is X^2 - 6X^2 + 14X + 24 = 0. We need to find the roots of this equation in the ratio 3:2. Let's assume the roots are 3k and 2k.
Sum and Product of Roots
The sum of the roots of a quadratic equation Ax^2 + Bx + C = 0 is given by -B/A and the product of the roots is given by C/A. In this case, the sum of the roots is -(-6) = 6 and the product of the roots is 24.
Using the Ratio of Roots
If the roots are in the ratio 3:2, we can write the sum and product of roots in terms of k. The sum becomes 3k + 2k = 5k and the product becomes 3k * 2k = 6k^2.
Solving for k
From the given sum and product, we have:
5k = 6 and 6k^2 = 24.
Solving these equations, we get k = 6/5 and k = 2.
Calculating the Roots
Now, substitute k back into the roots:
First root = 3k = 3*(6/5) = 18/5
Second root = 2k = 2*2 = 4
Therefore, the roots of the equation X^2 - 6X^2 + 14X + 24 = 0 in the ratio of 3:2 are 18/5 and 4.
The given equation is X^2 - 6X^2 + 14X + 24 = 0. We need to find the roots of this equation in the ratio 3:2. Let's assume the roots are 3k and 2k.
Sum and Product of Roots
The sum of the roots of a quadratic equation Ax^2 + Bx + C = 0 is given by -B/A and the product of the roots is given by C/A. In this case, the sum of the roots is -(-6) = 6 and the product of the roots is 24.
Using the Ratio of Roots
If the roots are in the ratio 3:2, we can write the sum and product of roots in terms of k. The sum becomes 3k + 2k = 5k and the product becomes 3k * 2k = 6k^2.
Solving for k
From the given sum and product, we have:
5k = 6 and 6k^2 = 24.
Solving these equations, we get k = 6/5 and k = 2.
Calculating the Roots
Now, substitute k back into the roots:
First root = 3k = 3*(6/5) = 18/5
Second root = 2k = 2*2 = 4
Therefore, the roots of the equation X^2 - 6X^2 + 14X + 24 = 0 in the ratio of 3:2 are 18/5 and 4.
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The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2?
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The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2?.
The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The two roots of an equation X square - 6 X square + 14 x + 24 is equal to zero are in the ratio of 3 ^ 2?.
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