Question

Quadratic equations Unit Test.
Assuming an equation with one side as a squared variable expression and the other side as a numeric.
statement #1: If the numeric expression is zero, there are two solutions.
Statement # 2: If the numeric expression is zero, there is one solution.
Statement # 3: If the numeric expression is zero, there are no solutions.
Statement # _____ is correct.

Answer 1

In a quadratic equation of the form \( (ax + b)^2 = c \), we can analyze the situation when \( c = 0 \):

1. If the equation is written as \( (ax + b)^2 = 0 \), we can solve for \( ax + b \) by taking the square root of both sides:
\[
ax + b = 0
\]
This means there is only one solution for \( x \) since we can solve for \( x \) directly:
\[
ax = -b \implies x = -\frac{b}{a}
\]

Therefore, when the numeric expression on one side is zero, there is one solution.

Thus:
- **Statement #1** (two solutions) is incorrect.
- **Statement #2** (one solution) is correct.
- **Statement #3** (no solutions) is incorrect.

**Correct answer:** Statement #2 is correct.