2024 · Q8
If 2 is a zero of the polynomial p(x) = x³ + 3x² - 6x - a, then what is the sum of the squares of the other zeros of the polynomial?
Elementary MathematicsAlgebra
- A10
- B17
- C21
- D37
Explanation
Since x = 2 is a zero, p(2) = 8 + 12 − 12 − a = 0 gives a = 8. Dividing x³ + 3x² − 6x − 8 by (x − 2) leaves x² + 5x + 4 = (x + 1)(x + 4), so the other zeros are −1 and −4. Their squares add to 1 + 16 = 17, option (b).