Question

2x² - 3x - 1 = 0

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=2$, $b=-3$, $c=-1$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$\Delta=b^2-4ac=(-3)^2-4(2)(-1)=9+8=17$

Step4: Substitute into formula

$x=\frac{-(-3)\pm\sqrt{17}}{2(2)}=\frac{3\pm\sqrt{17}}{4}$

Answer:

$x=\frac{3+\sqrt{17}}{4}$ and $x=\frac{3-\sqrt{17}}{4}$