What is the product of the roots of 6x² + 5x − 14 = 0?

Correct answer: −7/3

The governing concept is Vieta’s product relation. For a quadratic equation ax² + bx + c = 0 with roots α and β, the product of the roots is αβ = c/a. Comparing 6x² + 5x − 14 = 0 with the standard form gives a = 6 and c = −14. Therefore αβ = −14/6 = −7/3 after dividing numerator and denominator by 2. Hence option A is correct. There is no need to calculate either root separately. Option B has the correct magnitude but an incorrect positive sign; the negative constant term makes the product negative because a is positive. Options C and D incorrectly use the coefficient b = 5, whereas b determines the sum of the roots, not their product. The relation is valid even when the roots are not explicitly found.