Question

Show that the roots of the equation $x^2-2x+3=0$ are imaginary.

Answer 1

Given quadratic equation:

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

If $D<0$, then roots will be imaginary.

$D=b^2-4ac$

$=(-2{)}^2-4\times 1\times 3$

$=4-12$

$=-8$

$D=-8<0$

Therefore, roots are imaginary.