Answer to Question #91449 in Linear Algebra for Ra

Question

|2 3 7 |
If |1 x -2 | = 5, find x.
|0 2 x |

Answer 1

determinant is:

$2∗x∗x+3∗0∗(−2)+7∗1∗2−7∗x∗0−1∗3∗x−2∗2∗(−2)=5$

$2x^2 - 3x +17 = 0$

$\Delta = (-3)^2 - 4*2*17 = -127$

$\sqrt\Delta = \pm i\sqrt{127}$

$x = {3 \pm i\sqrt{127} \over 4}$ or $x = {3 \over 4} \pm {\sqrt{127} \over 4}i$