Matrices & Determinants
Determinant as polynomial
Grade 12
Question:
<p>Let \(px^4 + qx^3 + rx^2 + sx + t = \begin{vmatrix} x+1 & -2x & x-4 \\ x^2+3x & x-1 & x+3 \\ x-3 & x+4 & 3x \end{vmatrix}\), where \(p, q, r, s\) and \(t\) are constants, then \(t\) is equal to</p>
<p>(a) 0</p>
<p>(b) 1</p>
<p>(c) 2</p>
<p>(d) –1</p>
Step-by-Step Solution
Key Concept: The constant term of a polynomial obtained from a determinant equals the determinant value at x = 0.
<p>The constant term \(t\) in the polynomial equals the determinant evaluated at \(x = 0\). Substitute \(x = 0\) in the matrix and compute the determinant to get \(t = -1\).</p>
Correct Answer: D