Question

Find the roots of the following quadratic equations:

$x^2-2\sqrt{3}x+2=0$

Answer 1

Step 1:

Find the two roots of the quadratic equation:

Compare given quadratic equation with$a{x}^2+bx+c=0$, we get

$a=1,b=-2\sqrt{3},c=2$

Now, using quadratic formula:

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4\times a\times c}}{2a} \\ \Rightarrow x=\frac{-\left(-2\sqrt{3}\right)\pm \sqrt{{\left(-2\sqrt{3}\right)}^2-4\times 1\times 2}}{2\times 1} \\ \Rightarrow x=\frac{2\sqrt{3}\pm \sqrt{12-8}}{2\times 1} \\ \Rightarrow x=\frac{2\sqrt{3}\pm \sqrt{4}}{2\times 1} \\ \Rightarrow x=\frac{2\sqrt{3}\pm 2}{2\times 1} \\ \Rightarrow x=\frac{2\left(\sqrt{3}\pm 1\right)}{2\times 1} \\ \Rightarrow x=\sqrt{3}\pm 1 \\ \therefore x=\sqrt{3}+1,\sqrt{3}-1 \end{gathered}$$

Final Answer:

The roots of the quadratic equation are $\sqrt{3}+1,\sqrt{3}-1$.