Given the quadratic equation 2x² - 5x + b = 0, if its roots are in the ratio 2:3, what is the value of b?

Explanation

Let the roots be 2k and 3k. Their sum is 2k + 3k = 5k, which equals 5/2 (since sum of roots = 5/2 from -(-5)/2). Solving for k gives k = 1/2. The product of the roots is (2k)(3k) = 6k², which equals b/2 (from c/a = b/2). Substituting k = 1/2, we get b/2 = 6 * (1/2)² = 6 * 1/4 = 3/2, so b = 3. Thus, the value of b is 3.