Question

x^2-x+2=0 what is value of x?

Answer 1

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Answer 2

${x}^{2} - x + 2 = 0 \\ \\ determinant = {b}^{2} - 4ac \\ = {( - 1)}^{2} - 4 \times 2 \times 1 \\ = 1 - 8 \\ = - 7 \\ \\ since \: determinant \: is \: negative \\ it \: will \: have \: complex \: solutions \\ \\ x = \frac{ - b \pm \sqrt{{b}^{2} - 4ac} }{2a}$

$x = \frac{ - ( - 1) \pm \sqrt{ - 7} }{2 \times 1} \\ \\ x = \frac{1 \pm i \sqrt{7} }{2} \\ \\ \boxed{ \large{{x = \frac{1 + i \sqrt{7} }{2} \: \: and \: \: x = \frac{1 - i \sqrt{7} }{2}}}}$