Question

Solve the quadratic equation $x^2 - 5x - 10 = 0$ and give your answer correct to two decimal places.

Hint:

For quadratic equations, use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ and round final answers as required.

Answer 1

Using the Quadratic Formula
For a quadratic equation \(ax^2 + bx + c = 0\), the solution is given by the formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here,
\(a = 1\), \(b = -5\), \(c = -10\)

Substituting the values
\[ x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-10)}}{2(1)} \] \[ x = \frac{5 \pm \sqrt{25 + 40}}{2} \] \[ x = \frac{5 \pm \sqrt{65}}{2} \] \[ \sqrt{65} \approx 8.06 \]

Finding the two roots
\[ x = \frac{5 + 8.06}{2} = \frac{13.06}{2} \approx 6.53 \] \[ x = \frac{5 - 8.06}{2} = \frac{-3.06}{2} \approx -1.53 \]

Final Answer
The solutions of the equation correct to two decimal places are:
\(x \approx 6.53\) and \(x \approx -1.53\).