Question

Solving the following quadratic equation by factorization, the roots are :$2,-\frac{5}{16}$
$16x-\frac{10}{x}=27$

• A. True
• B. False

Answer 1

The correct option is A True

$16x-\frac{10}{x}=27$

$\Rightarrow$ $16x^2-10=27x$

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

$\Rightarrow$ $16x^2-32x+5x-10=0$

$\Rightarrow$ $16x(x-2)+5(x-2)=0$

$\Rightarrow$ $(x-2)(16x+5)=0$

$\Rightarrow$ $x-2=0$ and $16x+5=0$

$\therefore$ $x=2$ and $x=-\frac{5}{16}$

$\therefore$ $2,-\frac{5}{16}$ are roots of the given quadratic equation $16x-\frac{10}{x}=27$, is true.