Solve: x² + 4x + 4 = 0 and identify the nature of roots
A
Two distinct real roots
B
One repeated real root
C
Two complex roots
D
No roots
Correct Answer: Option B — One repeated real root
Explanation:
Discriminant = b²-4ac = 16-16 = 0. When D=0 there is exactly one repeated root: x = -b/2a = -4/2 = -2. This is a perfect square trinomial (x...
Discriminant = b²-4ac = 16-16 = 0. When D=0 there is exactly one repeated root: x = -b/2a = -4/2 = -2. This is a perfect square trinomial (x+2)² = 0. Recognizing perfect square quadratics allows instant factoring and reveals repeated roots without computing the full quadratic formula.