If the sum of the roots of the equation 2x² + 5x + k = 0 is -2.5, find the product of the roots

Explanation

For a quadratic equation ax² plus bx plus c equals 0, the sum of roots equals negative b over a. Given sum equals negative 2.5, verify: negative 5 over 2 equals negative 2.5. This confirms the equation parameters are correct.

The product of roots for a quadratic equation equals c over a. In this equation, a equals 2 and c equals k. Therefore, the product of roots equals k over 2.

The question asks for the product without needing to find k specifically. Using Vieta formulas, the product is k over 2 regardless of the actual value of k. This is the general answer.