16Hit1600
Advanced MathHardProduct of all real solutions of a quartic in x²

Advanced Math practice question

The equation x⁴ − 10x² + 9 = 0 has four real solutions. What is the product of the four solutions?

Answer: 9

Let u = x²: u² − 10u + 9 = (u − 1)(u − 9) = 0, so x = ±1 and x = ±3. Their product is (1)(−1)(3)(−3) = 9.

Common wrong answers

If you answered 0
0 is the sum of the solutions, not the product.
If you answered 3
3 is the product of the two positive solutions only.
If you answered -9
−9 gets the sign wrong; two negative factors make the product positive.

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