Determine the natura of the roots of the equation (2) \( x^{2}-3 x-2=0 \)

Solve the equation \( x^{2}-3x-2=0 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}-3x-2=0\) - step1: Solve using the quadratic formula: \(x=\frac{3\pm \sqrt{\left(-3\right)^{2}-4\left(-2\right)}}{2}\) - step2: Simplify the expression: \(x=\frac{3\pm \sqrt{17}}{2}\) - step3: Separate into possible cases: \(\begin{align}&x=\frac{3+\sqrt{17}}{2}\\&x=\frac{3-\sqrt{17}}{2}\end{align}\) - step4: Rewrite: \(x_{1}=\frac{3-\sqrt{17}}{2},x_{2}=\frac{3+\sqrt{17}}{2}\) The roots of the equation \(x^{2}-3x-2=0\) are \(x_{1}=\frac{3-\sqrt{17}}{2}\) and \(x_{2}=\frac{3+\sqrt{17}}{2}\). Since the roots are real and distinct, the nature of the roots is real and distinct.