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Given that a^2 + b^2 + c^2 = -2 and f(x) = \left|\begin{matrix} 1+a^2x & (1+b^2)x & (1+c^2)x \\ (1+a^2)x & 1+b^2x & (1+c^2)x \\ (1+a^2)x & (1+b^2)x & 1+c^2x \end{matrix}\right|, what is the degree of the polynomial f(x)?
- 1
- 0
- 3
- 2
Correct answer: 0
Solution
The determinant f(x) simplifies to a constant value because the terms involving x cancel out due to the specific relationship between a, b, and c, resulting in a polynomial of degree 0.
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