46. Which statement best describes why an equation with a discriminant of zero has one distinct real root?
A Consider the quadratic equation. When the discriminant is zero, the distinct real root is zero.
B Consider the quadratic equation. When the discriminant is zero, the equation is reduced to
\[
x=\frac{ \pm \sqrt{b^{2}-4 a c}}{2 a}
\]
C Consider the quadratic equation. When the discriminant is zero, the equation is reduced to $x=\frac{-b \pm 0}{2 a}$, or $x=\frac{-b}{2 a}$
D Consider the quadratic equation. When the discriminant is zero, the equation is reduced to $x=\frac{b \pm 0}{2 a}$, or $x=\frac{b}{2 a}$
Answer
\(\boxed{\text{C}}\)
Step 1 ：Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Step 2 ：Identify the discriminant: \(D = b^2 - 4ac\)
Step 3 ：When the discriminant is zero, the square root becomes zero: \(x = \frac{-b \pm 0}{2a}\)
Step 4 ：Simplify the equation: \(x = \frac{-b}{2a}\)
Step 5 ：Compare with the given options and find the match
Step 6 ：\(\boxed{\text{C}}\)
