Question

Find the roots of the equation $16x^2-27x-10=0$.

Answer 1

$16x^2-27x-10=0$

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

$a=16,b=-27,c=-10$

The roots can be found using the formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\therefore x=\frac{27\pm \sqrt{(27{)}^2-4\times 16\times (-10)}}{2\times 16}$

$=\frac{27\pm \sqrt{1369}}{32}=\frac{27\pm 37}{32}=\frac{64}{32},\frac{-10}{32}$

$\therefore$ The roots are $\frac{-5}{16}$ and $2$.