Matrices & Determinants
Properties of determinants
Grade Class 12

Question:

If a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> = -2 and f(x) = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
(A) 0
(B) 1
(C) 2
(D) 3

Step-by-Step Solution

Key Concept: The determinant can be expressed as a product of two matrices. Since the rows are identical in form, the determinant is zero for all x.
The given determinant has rows that are identical in form. Specifically, each row is of the form [1+a^2x, 1+b^2x, 1+c^2x]. Since all three rows are identical, the determinant is 0 for any value of x. Thus, f(x) = 0, which is a polynomial of degree 0.
Correct Answer: 1

Master Matrices & Determinants with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free