Matrices & Determinants
Determinants
Grade 12
Question:
<p>Sum of real roots of the equation <span style='display:inline-block; border: 1px solid black; padding: 5px;'>\[\begin{vmatrix} 1 & 4 & 20 \\ 1 & 2 & 5 \\ 1 & 2x & 5x^2 \end{vmatrix} = 0\]</span> is</p>
<p>(a) \(-2\)</p>
<p>(b) \(-1\)</p>
<p>(c) \(0\)</p>
<p>(d) \(1\)</p>
Step-by-Step Solution
Key Concept: Evaluate the determinant as a polynomial equation in x and find the sum of its real roots.
<p>Expand the determinant and set equal to zero. The equation will yield real roots whose sum can be found using Vieta's formulas or by solving directly.</p>
Correct Answer: B