Question

Find the roots of the following quadratic equations:

$0.3x^2-0.1x-0.4=0$

Answer 1

Step 1:

Simplify quadratic equation:

$$\begin{gathered} 0.3x^2-0.1x-0.4=0 \\ \Rightarrow 3x^2-x-4=0\left[\mathrm{Multiply}\mathrm{by}10\right] \end{gathered}$$

Step 2:

Find the two roots of the quadratic equation:

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

we get, $a=3,b=-1,c=-4$

Now, using quadratic formula:

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4\times a\times c}}{2a} \\ \Rightarrow x=\frac{-\left(-1\right)\pm \sqrt{{\left(-1\right)}^2-4\times 3\times -4}}{2\times 3} \\ \Rightarrow x=\frac{1\pm \sqrt{1+48}}{2\times 3} \\ \Rightarrow x=\frac{1\pm \sqrt{49}}{2\times 3} \\ \Rightarrow x=\frac{1\pm 7}{6} \\ \Rightarrow x=\frac{1+7}{6},\frac{1-7}{6} \\ \Rightarrow x=\frac{8}{6},\frac{-6}{6} \\ \therefore x=\frac{4}{3},-1 \end{gathered}$$

Final Answer:

The roots of the quadratic equation are $\frac{4}{3},-1$.