Question

Solve each of the following quadratic equations:

$5x^2+13x+8=0$ [CBSE 2013C]

Answer 1

We write, 13x = 5x + 8x as $5x^2\times 8=40x^2=5x\times 8x$
$$\begin{gathered} \therefore 5x^2+13x+8=0 \\ \Rightarrow 5x^2+5x+8x+8=0 \\ \Rightarrow 5x\left(x+1\right)+8\left(x+1\right)=0 \\ \Rightarrow \left(x+1\right)\left(5x+8\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x+1=0\mathrm{or}5x+8=0 \\ \Rightarrow x=-1\mathrm{or}x=-\frac{8}{5} \end{gathered}$$
Hence, $-1$ and $-\frac{8}{5}$ are the roots of the given equation.