Advanced MathHardReal solutions of a quadratic in x²
Advanced Math practice question
How many real solutions does the equation x⁴ − 5x² + 4 = 0 have?
Answer: 4
Treat x² as the variable: (x²)² − 5(x²) + 4 = 0 factors as (x² − 1)(x² − 4) = 0. So x² = 1 or x² = 4, giving x = ±1 and x = ±2 — four real solutions.
Common wrong answers
- If you answered 0
- Both x² = 1 and x² = 4 have real solutions, so the equation certainly does.
- If you answered 1
- 1 would mean a single solution; the equation has four.
- If you answered 2
- 2 counts the two values of x² (1 and 4) but each gives two values of x.
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