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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