ExamBro
ExamBro
CUET · MATHS · PYQ PAPER 2023

The value of the determinant \(\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|\) is:

  1. A Zero
  2. B a + b + c - 3abc
  3. C (a - b)(b - c)(a - c)
  4. D \(a^2+b^2+c^2-a b c\)
Verified Solution

Answer & Solution

Correct Answer

(C) (a - b)(b - c)(a - c)

Step-by-step Solution

Detailed explanation

\(\left| \begin{array}{lll} a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1 \end{array} \right| = a^2(b \cdot 1 - 1 \cdot c) - a(b^2 \cdot 1 - 1 \cdot c^2) + 1(b^2 \cdot c - b \cdot c^2)\) \(= a^2(b-c) - a(b^2-c^2) + bc(b-c)\) \(= a^2(b-c) - a(b-c)(b+c) + bc(b-c)\)…