16Hit1600
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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