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?

Question

Answer

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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