Question

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

• A. $24/25$
• B. $-12/25$
• C. $12/25$
• D. $20/25$

Answer 1

The correct option is A $24/25$

Rewriting the equation ;

$25x^2+20x-15x+12=0$

$\Rightarrow 5x(5x+4)-3(5x+4)=0$

$\Rightarrow (5x+4)(5x-3)=0$

$\therefore x=\frac{-4}{5}orx=\frac{3}{5}$

As $x>0\Rightarrow$ $x=4/5=$ $\text{cos}\alpha$

$\Rightarrow \text{sin}\alpha =3/5$

$\therefore \text{sin}2\alpha =2\text{sin}\alpha \text{cos}\alpha$

$\Rightarrow \text{sin}2\alpha =2\times 3/5\times 4/5$

$\therefore \text{sin}2\alpha =24/25$