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If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.
- a)5/6
- b)1/6
- c)-5/6
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4...
The sum of the roots of a quadratic equation ax2 + bx + c is -b / a
-(2m - 1) / m = 6 / (3m + 1) - 6m2 + m + 1 = 6m - 6m2 - 5m + 1 = 0 m = -1 or 1/6 Thus, the sum of the values of m = -(5/6) Hence, option 3.
Most Upvoted Answer
If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4...
Sum of roots for equation a(x*x)+bx+c=0 will be -b/a. so, now we get those two equation sum of roots as (1-2m)/m and 6/(3m+1) now equating them we get an equation as 6(m*m)+5m-1=0 on solving we get m values as -1 and 1/6 upon so adding them up we will get -5/6.
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Community Answer
If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4...
To find the sum of the values of m, we need to equate the sum of the roots of the two quadratic equations given.
Let's consider the first quadratic equation:
mx^2 + (2m - 1)x + 4 = 0
The sum of the roots of this equation can be found using the formula:
Sum of roots = -B/A,
where A, B, and C are the coefficients of the quadratic equation.
In this case, A = m, B = (2m - 1), and C = 4.
So, the sum of the roots of the first equation is:
Sum of roots = -B/A = -(2m - 1)/m = (1 - 2m)/m
Now, let's consider the second quadratic equation:
(3m - 1)x^2 - 6x + (2m - 3) = 0
Again, using the formula for the sum of roots, we have:
Sum of roots = -B/A,
where A = (3m - 1), B = -6, and C = (2m - 3).
So, the sum of the roots of the second equation is:
Sum of roots = -B/A = -(-6)/(3m - 1) = 6/(3m - 1) = 6/(1 - 3m)
Since we are given that the sum of the roots of the two equations is equal, we can equate them:
(1 - 2m)/m = 6/(1 - 3m)
Now, we can solve this equation to find the value of m.
Cross-multiplying, we get:
(1 - 2m)(1 - 3m) = 6m
Expanding the equation, we have:
1 - 3m - 2m + 6m^2 = 6m
Rearranging terms, we get:
6m^2 + m - 6m + 1 - 6m = 0
Simplifying, we have:
6m^2 - 11m + 1 = 0
Now, we can solve this quadratic equation for the values of m.
Using the quadratic formula, we have:
m = (-B ± √(B^2 - 4AC))/(2A)
Substituting the values of A, B, and C, we get:
m = (-(-11) ± √((-11)^2 - 4(6)(1)))/(2(6))
Simplifying further, we have:
m = (11 ± √(121 - 24))/(12)
m = (11 ± √97)/12
Therefore, the sum of the values of m is:
(11 + √97)/12 + (11 - √97)/12 = 22/12 = 11/6
Hence, the correct answer is option C) -5/6.
Let's consider the first quadratic equation:
mx^2 + (2m - 1)x + 4 = 0
The sum of the roots of this equation can be found using the formula:
Sum of roots = -B/A,
where A, B, and C are the coefficients of the quadratic equation.
In this case, A = m, B = (2m - 1), and C = 4.
So, the sum of the roots of the first equation is:
Sum of roots = -B/A = -(2m - 1)/m = (1 - 2m)/m
Now, let's consider the second quadratic equation:
(3m - 1)x^2 - 6x + (2m - 3) = 0
Again, using the formula for the sum of roots, we have:
Sum of roots = -B/A,
where A = (3m - 1), B = -6, and C = (2m - 3).
So, the sum of the roots of the second equation is:
Sum of roots = -B/A = -(-6)/(3m - 1) = 6/(3m - 1) = 6/(1 - 3m)
Since we are given that the sum of the roots of the two equations is equal, we can equate them:
(1 - 2m)/m = 6/(1 - 3m)
Now, we can solve this equation to find the value of m.
Cross-multiplying, we get:
(1 - 2m)(1 - 3m) = 6m
Expanding the equation, we have:
1 - 3m - 2m + 6m^2 = 6m
Rearranging terms, we get:
6m^2 + m - 6m + 1 - 6m = 0
Simplifying, we have:
6m^2 - 11m + 1 = 0
Now, we can solve this quadratic equation for the values of m.
Using the quadratic formula, we have:
m = (-B ± √(B^2 - 4AC))/(2A)
Substituting the values of A, B, and C, we get:
m = (-(-11) ± √((-11)^2 - 4(6)(1)))/(2(6))
Simplifying further, we have:
m = (11 ± √(121 - 24))/(12)
m = (11 ± √97)/12
Therefore, the sum of the values of m is:
(11 + √97)/12 + (11 - √97)/12 = 22/12 = 11/6
Hence, the correct answer is option C) -5/6.
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If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the roots of the quadratic equations mx2 + (2m - 1)x + 4 and (3m + 1)x2 - 6x + (2m - 3) are equal, then find the sum of values of m.a)5/6b)1/6c)-5/6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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