Matrices & Determinants
Determinant expansion
Grade 12
Question:
<p>There are two numbers x making the \[ \begin{vmatrix} 1 & -2 & 5 \\ & 2 & x & -1 \\ & 0 & 4 & 2x \end{vmatrix} \] equal to 86. The sum of these numbers is:</p>
<p>(A) -4</p>
<p>(B) 5</p>
<p>(C) -3</p>
<p>(D) 9</p>
Step-by-Step Solution
Key Concept: Convert determinant into quadratic \to use sum of roots (-b/a) instead of solving fully.
1. **Expand determinant** along first row
2. **Form equation**: 2x^2 + 8x - 42 = 0
3. **Simplify**: x^2 + 4x - 21 = 0
4. **Sum of roots**: -$b/a$ = -4
Correct Answer: 1