Question

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

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

Answer 1

The correct option is D $-\frac{24}{25}$

We can write the equation as $(5x+4)(5x-3)=0$
Now $x$ lies between $0$ and $-1$ so $\cos \alpha =-\frac{4}{5}$
Hence, $\sin \alpha =\frac{3}{5}$
$\sin \left(2\alpha \right)=2(-\frac{4}{5})\left(\frac{3}{5}\right)=-\frac{24}{25}$
Option D is correct.