Advanced MathMediumZeros of a biquadratic function
Advanced Math practice question
The function f(x) = x⁴ − 20x² + 64 has four real zeros. What is the sum of the two largest zeros?
Answer: 6
With u = x²: (u − 4)(u − 16) = 0, so x = ±2 and ±4. The two largest zeros are 4 and 2, summing to 6.
Common wrong answers
- If you answered 0
- 0 is the sum of all four zeros; the two largest sum to 6.
- If you answered 8
- The largest zeros are 4 and 2 — their product is 8, their sum 6.
- If you answered 20
- 20 is the sum of the x² values (4 + 16), not of the zeros.
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