Question

Let $A = \begin{bmatrix} -2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1 \end{bmatrix}$. If the roots of the equation $\det A = 0$ are $l, m$ then $l^3 - m^3 =$

• A. $35$
• B. $-35$
• C. $19$
• D. $-19$

Hint:

Use factorization identities to simplify expressions involving roots of equations derived from determinants.

Answer 1

The Correct Option is B

Compute determinant of $A$ as a function of $x$.
Find the roots $l$ and $m$ such that $\det A = 0$.
Using identity $l^3 - m^3 = (l - m)(l^2 + lm + m^2)$, evaluate based on roots found.
Given correct answer: $-35$