The nature of the roots of the equation x² - 5x + 7 = 0 is

For how many different values of $a$ does the following system have at least two distinct solutions?

$ax+y=0$

$x+\left(a+10\right) y=0$

Two equations are given, you have to solve both the equations and get the answer:

$\left(i\right) X^2-X-6=0$

$\left(ii\right) Y^2-6Y+8=0$

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 :

Two equations are given, you should solve both the equations and get the answer:

$\left(i\right) X^2-11X+24=0$

$\left(ii\right) Y^2+14Y-45+0$

Two equations are given, you have to solve both the equations and get the answer:

$\left(i\right) 2X^2-4X+2=0$

$\left(ii\right) 2Y^2-Y-1=0$

Two equations are given, you have to solve both the equations and should get the answer:

$\left(i\right) X^2-15X+56=0$

$\left(ii\right) Y=\sqrt{64}$

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. $(x - 12) (x + 11)$