If b^2 - 4ac = 0, what is the nature of the roots?

If b^2 - 4ac = 0, what is the nature of the roots?

• A. b^2 - 4ac > 0
• B. b^2 - 4ac = 0
• C. a^2 + b^2 = c^2
• D. b^2 - 4ac < 0

Answer: (B)

Discriminant concept: for a quadratic ax^2 + bx + c = 0, the value b^2 − 4ac tells how many roots there are and what kind they are. If the discriminant is zero, there is exactly one real root, but it appears twice—a double root. Using the quadratic formula, the roots are x = [-b ± sqrt(b^2 − 4ac)]/(2a). When the discriminant is zero, the square root term vanishes, giving x = −b/(2a) as the single root, repeated. So the nature of the roots here is a single real root with multiplicity two. The other listed idea (a^2 + b^2 = c^2) is unrelated to the roots and comes from a different context.

Discriminant concept: for a quadratic ax^2 + bx + c = 0, the value b^2 − 4ac tells how many roots there are and what kind they are. If the discriminant is zero, there is exactly one real root, but it appears twice—a double root. Using the quadratic formula, the roots are x = [-b ± sqrt(b^2 − 4ac)]/(2a). When the discriminant is zero, the square root term vanishes, giving x = −b/(2a) as the single root, repeated. So the nature of the roots here is a single real root with multiplicity two. The other listed idea (a^2 + b^2 = c^2) is unrelated to the roots and comes from a different context.