16Hit1600
Advanced MathVery hardCounting distinct real roots of a cubic

Advanced Math practice question

How many distinct real solutions does the equation x³ − 4x² + 4x = 0 have?

Answer: 2

x(x² − 4x + 4) = x(x − 2)² = 0, so x = 0 or x = 2: two distinct solutions.

Common wrong answers

If you answered 0
The equation clearly has x = 0 as a solution.
If you answered 1
1 misses x = 0.
If you answered 3
3 counts the repeated root x = 2 twice.

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