If the equation $2{\mathrm{x}}^2-7\mathrm{x}+12=0$ has two roots $\alpha$ and $\beta ,$ then the value of $\frac{\alpha }{\beta }+\frac{\mathrm{\beta }}{\mathrm{\alpha }}$ is:

The sum of the roots of the equation, $x+1-2{\log }_2\left(3+2^x\right)+2{\log }_4\left(10-2^{-x}\right)=0,$ is :

Find the sum of all real value of $x$,which satisfies

$\frac{1}{x^2-10x-45}+\frac{1}{x^2-10x-29}=\frac{2}{x^2-10x-69}$

The factors of equation $x^2+7x+12=0$  are-

(A) -3 and -4 

(B) 3 and -4 

(C) -3 and 4 

(D) 3 and 4 

FInd the factors of $(x^2 - x - 132):$

1. $(x - 11) (x -12)$
2. $(x + 12) (x -11)$
3. $(x + 11) (x + 12)$
4. $(x - 12) (x + 11)$