16Hit1600
Advanced MathVery hardQuartic equation that is quadratic in x²

Advanced Math practice question

What is the sum of the positive solutions of x⁴ − 13x² + 36 = 0?

Answer: 5

Let u = x²: u² − 13u + 36 = 0 → (u − 4)(u − 9) = 0 → x² = 4 or x² = 9. The positive solutions are 2 and 3, whose sum is 5.

Common wrong answers

If you answered 0
0 is the sum of all four solutions (±2, ±3).
If you answered 6
6 is 2 × 3, the product.
If you answered 13
13 is the sum of x² values (4 + 9), not of x values.

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