If the roots of x² − 6x + k = 0 are equal, what is k?

Correct answer: 9

The governing concept is the discriminant. For ax² + bx + c = 0, equal real roots occur exactly when D = b² − 4ac = 0. In x² − 6x + k = 0, a = 1, b = −6 and c = k. Therefore D = (−6)² − 4(1)(k) = 36 − 4k. Setting this equal to zero gives 36 − 4k = 0, so 4k = 36 and k = 9. Hence option B is correct. The value 6 in option A confuses the coefficient with the required constant, while 12 and 36 result from incomplete or incorrect use of the discriminant condition. When D is zero, the repeated root itself is −b/(2a) = 3, but the question asks for k, not the root.