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.

Q: Answer-The roots of the quadratic equation x² + px + q = 0 are in the ratio 3:4. If the sum and product of...

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 x 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