Question

The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for

• A. 3 values of \( x \)
• B. 1 value of \( x \)
• C. 2 values of \( x \)
• D. No value of \( x \)

Hint:

A determinant vanishes when its rows or columns are linearly dependent. Check for this condition when solving problems.

Answer 1

The Correct Option is D

Step 1: Determine the condition for determinant to vanish.
For the determinant to vanish, the rows or columns must be linearly dependent. In this case, there is no value of \( x \) that satisfies this condition.
Step 2: Conclusion.
The determinant does not vanish for any specific value of \( x \). Final Answer: \[ \boxed{\text{No value of } x} \]