Question

1. $x^2 - 3x + 3 = 0$

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = -3\), \(c = 3\).

Step2: Calculate discriminant

Discriminant \(D = b^2 - 4ac\). Substitute values: \(D = (-3)^2 - 4\times1\times3 = 9 - 12 = -3\).

Step3: Use quadratic formula

Quadratic formula: \(x = \frac{-b \pm \sqrt{D}}{2a}\). Since \(D = -3\), \(\sqrt{D} = \sqrt{-3} = i\sqrt{3}\) (where \(i\) is imaginary unit). Substitute \(a\), \(b\), \(D\): \(x = \frac{3 \pm i\sqrt{3}}{2}\).

Answer:

The solutions are \(x = \frac{3 + i\sqrt{3}}{2}\) and \(x = \frac{3 - i\sqrt{3}}{2}\)