If a^2 + b^2 + c^2 = -2 and f(x) = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|"><mtable><mtr><mtd><mn>1</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mi>x</mi></mtd><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd></mtr><mtr><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd><mtd><mn>1</mn><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mi>x</mi></mtd><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd></mtr><mtr><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd><mtd><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo><mi>x</mi></mtd><mtd><mn>1</mn><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mi>x</mi></mtd></mtr></mtable></mfenced></math> then f(x) is a polynomial of degree-
Step-by-Step Solution
Key Concept: The determinant can be simplified by performing row operations. Since the sum of the squares is -2, the determinant evaluates to a constant, making it a polynomial of degree 0.
Performing row operations R1 -> R1 - R2 and R2 -> R2 - R3, we can simplify the determinant. Given a^2 + b^2 + c^2 = -2, the expression simplifies to a constant value independent of x.
Correct Answer: A