16Hit1600
Advanced MathEasy–MediumCounting solutions of a perfect-square equation

Advanced Math practice question

How many distinct real solutions does the equation x² + 6x + 9 = 0 have?

Answer: 1

x² + 6x + 9 = (x + 3)², so the equation is (x + 3)² = 0, which is true only when x = −3. One distinct solution.

Common wrong answers

If you answered 0
The equation does have a solution: x = −3 gives 9 − 18 + 9 = 0.
If you answered 2
2 is the usual count for a quadratic, but here both roots coincide at x = −3.
If you answered 3
3 is the number in the factor (x + 3), not a count of solutions.

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