What is the nature of the roots of x² + 6x + 9 = 0?

Correct answer: Two equal real roots

Answer: B, two equal real roots. For ax² + bx + c = 0, the discriminant is D = b² − 4ac. Here a = 1, b = 6, and c = 9, so D = 6² − 4(1)(9) = 36 − 36 = 0. The criterion is: D > 0 gives two distinct real roots, D = 0 gives two equal real roots, and D < 0 gives no real roots in the real number system. We can verify the result by factorising: x² + 6x + 9 = (x + 3)². Thus (x + 3)² = 0 gives x = −3 twice, so the repeated root is real and equal. A would require a positive discriminant. C would require a negative discriminant. D is impossible because a quadratic has at most two roots. Memory cue: zero discriminant means the parabola touches the x-axis once, representing one repeated real root.