If $0<A<\frac{\pi }{2}$ and $\sin A+\cos A+\tan A+\cot A+\sec A+\cos ecA=7,\sin A$ and $\cos A$ are roots of equation $4x^2-3x+\alpha =0,$ then the value of $\left|\frac{25\alpha }{4}\right|$ is

Given equation is $4x^2-3x+\alpha =0$  
sinA and cosA are its roots, then 
$\sin A+\cos A=\frac{3}{4}$ 
$\sin A\cos A=\frac{\alpha }{4}$ 
Now, $\sin A+\cos A+\tan A+\cot A+\sec A+\cos ecA=7$
$\Rightarrow \frac{3}{4}+\frac{1+(\sin A+\cos A)}{\sin A\cos A}=7\Rightarrow \frac{1+\frac{3}{4}}{\frac{\alpha }{4}}=7-\frac{3}{4}$ 
$\therefore \frac{25\alpha }{4}=7$