What is the nature of the roots of x² − 9x + 20 = 0?

Correct answer: Two real, rational, and distinct roots (D = 1)

For a quadratic equation Ax² + Bx + C = 0, the discriminant D = B² − 4AC determines the nature of its roots. Here A = 1, B = −9, and C = 20. Thus D = (−9)² − 4(1)(20) = 81 − 80 = 1. Since D is positive, the roots are real and distinct. Moreover, D = 1 is a perfect square, and with rational coefficients this means both roots are rational. Indeed, the equation factors as (x − 4)(x − 5) = 0, giving roots 4 and 5. Therefore option A is correct; D = 0 would indicate equal roots, while D < 0 would indicate no real roots.