Question

Evaluate \(\begin{vmatrix}8x+1&2x-2\\x^2-1&3x+5\end{vmatrix}\).

(a) -2x^3-26x^2+45x+3

(b) -2x^3+26x^2+45x+3

(c) -2x^3+26x^2+45x-3

(d) -2x^3-26x^2-45x+3

The question was asked by my college professor while I was bunking the class.

My enquiry is from Determinant in portion Determinants of Mathematics – Class 12

Answer 1

Correct choice is (b) -2x^3+26x^2+45x+3

The explanation: Expanding along the first row, we get

∆=8x+1(3x+5)-(2x-2)(x^2-1)

=(24x^2+43x+5)-(2x^3-2x^2-2x+2)

=-2x^3+26x^2+45x+3.