use quadratic formula to solve x^2-2x+3=0

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Remember quadratic formula of quadratic equation `ax^2 + bx + c = 0: ` `x_(1,2)=[-b+-sqrt(b^2-4ac)]/(2a)`

Compare the standard quadratic equation and your equation and you will find the values of a,b,c.

a=1,b=-2,c=3

Use substitution in quadratic formula:

`x_(1,2)=(-(-2)+-sqrt((-2)^2-4*1*3))/(2*1)`

`x_(1,2)=(2+-sqrt(4-12))/(2)`

`x_(1,2)=(2+-sqrt(-8))/(2)`

Use the fact that `sqrt(-1)=i ` (theory of complex number)

`x_(1,2)=(2+-2*i*sqrt(2))/(2)`

Reduce

`x_(1,2)=(1+-i*sqrt(2))`

ANSWER: The roots of quadratic equation are not real, but they are complex: `x_(1,2)=(1+-i*sqrt(2)).`

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