Question
The roots of the quadratic equation x² + px + q = 0 are
in the ratio 3:4. If the sum and product of the roots are 7 and 12, respectively, find the values of p and q.Solution
Let the roots of the equation be 3k and 4k. The sum of the roots = 3k + 4k = 7, so 7k = 7, giving k = 1. Thus, the roots are 3 and 4. The product of the roots = 3 × 4 = 12. For the quadratic equation x² + px + q = 0, the sum of the roots is -p, and the product of the roots is q. So, p = -7 and q = 12. Correct answer: b. p = -7, q = 12
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