Advanced MathEasy–MediumCounting distinct solutions of a perfect square
Advanced Math practice question
How many distinct real solutions does x² − 10x + 25 = 0 have?
- A. Exactly oneCorrect
- B. Exactly two
- C. None
- D. Infinitely many
Answer: A. Exactly one
The left side is (x − 5)², which is zero only at x = 5 — one distinct solution.
Why the other answers are wrong
- B. Exactly two
- Both factors are the same (x − 5), so the two roots coincide.
- C. None
- x = 5 does satisfy the equation.
- D. Infinitely many
- A nonzero quadratic cannot vanish everywhere.
More Advanced Math questions
- Easy–Medium
If f(x) = 2x² − 3, what is f(4)? - Easy–Medium
Which expression is equivalent to (2x³)(3x⁴)? - Easy–Medium
What are the solutions to x² − 16 = 0? - Easy–Medium
Which expression is equivalent to (x + 5)²? - Easy–Medium
For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
What are the solutions to the equation 2(x − 3)² − 32 = 0 ?
Not affiliated with the College Board. SAT is a trademark of the College Board.