Question

Find the value of x if

${\displaystyle \left|\begin{array}{cc}{x}^2-x+1& x+1\\ x+1& x+1\end{array}\right|}$ = 0

Answer 1

${\displaystyle \left|\begin{array}{cc}{x}^2-x+1& x+1\\ x+1& x+1\end{array}\right|}$ = 0

∴ (x² – x + 1)(x + 1) – (x + 1)(x + 1) = 0

∴ (x + 1)[x² – x + 1 – x – 1) = 0

∴ (x + 1)(x² – 2x) = 0

∴ x (x + 1)(x – 2) = 0

∴  x = 0 or x + 1 = 0 or x – 2 = 0

∴ x = 0, x = – 1, x = 2.