Question

find all complex solutions of $x^2 - 3x + 4 = 0$. (if there is more than one solution, separate them with commas.)

Explanation:

Step1: Identify quadratic coefficients

For $x^2 - 3x + 4 = 0$, $a=1$, $b=-3$, $c=4$

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = (-3)^2 - 4(1)(4) = 9 - 16 = -7$

Step3: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{\Delta}}{2a}$
Substitute values: $x = \frac{3 \pm \sqrt{-7}}{2(1)} = \frac{3 \pm i\sqrt{7}}{2}$

Answer:

$x = \frac{3 + i\sqrt{7}}{2}, \frac{3 - i\sqrt{7}}{2}$