Question

If $\cos \alpha$ is a root of the equation $25x^2+5x-12=0,-1<x<0,$ then the value of $\sin 2\alpha$ is

• A. $\frac{12}{25}$
• B. $\frac{-12}{25}$
• C. $\frac{24}{25}$
• D. $\frac{20}{25}$

Answer 1

The correct option is C $\frac{24}{25}$

$25x^2+5x-12=0\Rightarrow x=\frac{3}{5},\frac{4}{5}$

Now, if $\cos \alpha =\frac{3}{5}$ then $\sin \alpha =\sqrt{1-(\frac{3}{5}{)}^2}=\frac{4}{5}$

$\sin 2\alpha =2\sin \alpha \cos \alpha =2\ast \frac{3}{5}\ast \frac{4}{5}=\frac{24}{25}$

Similarly, if $\cos \alpha =\frac{4}{5}$ then $\sin \alpha =\sqrt{1-(\frac{4}{5}{)}^2}=\frac{3}{5}$

$\sin 2\alpha =2\sin \alpha \cos \alpha =2\ast \frac{3}{5}\ast \frac{4}{5}=\frac{24}{25}$

Therefore, Answer is $\frac{24}{25}$