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If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    6
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the roots of the equation 2x2- 5x + b = 0 are in the ratio of 2:3, ...
Let the roots of the equation 2a and 3a respectively.
2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2
Product of the roots: 6a2 = b/2 => b = 12a2
a = 1/2, b = 3.
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Most Upvoted Answer
If the roots of the equation 2x2- 5x + b = 0 are in the ratio of 2:3, ...
To find the value of b, we need to use the fact that the roots of the equation are in the ratio of 2:3.

Let's assume the roots of the equation are 2k and 3k, where k is a constant.

Using the sum and product of roots formulas, we can write the equation as follows:

Sum of roots: 2k + 3k = -(-5/2) = 5/2
Product of roots: (2k)(3k) = b/2

Simplifying the equations, we get:

5k = 5/2
6k^2 = b/2

Now, let's solve for k:

5k = 5/2
k = 1/2

Substituting the value of k in the second equation, we get:

6(1/2)^2 = b/2
6(1/4) = b/2
6/4 = b/2
3/2 = b/2
b = 3

Therefore, the value of b is 3, which corresponds to option A.
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If the roots of the equation 2x2- 5x + b = 0 are in the ratio of 2:3, then find the value of b?a)3b)4c)5d)6e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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