Question

solve the quadratic equation using the quadratic formula
0 = x² - x - 3
options:
x = \frac{2\pm\sqrt{11}}{1}
x = \frac{1\pm\sqrt{13}}{2}
x = \frac{2\pm\sqrt{13}}{1}
x = \frac{1\pm i\sqrt{11}}{2}

Explanation:

Step1: Identify coefficients

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

Step2: Apply Quadratic Formula

Quadratic Formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute values: \(x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-3)}}{2(1)}=\frac{1\pm\sqrt{1 + 12}}{2}=\frac{1\pm\sqrt{13}}{2}\).

Answer:

\(x=\frac{1\pm\sqrt{13}}{2}\) (the option with this expression, e.g., if it's the second option: B. \(x=\frac{1\pm\sqrt{13}}{2}\))