Find the roots of the equation: $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x\ne -4,7$.

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 difference of the squares of two positive numbers is $45$. The square of the smaller number is four times the larger number. Find the numbers.

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

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

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

Find the sum and the products of the roots of:

$3x^2-5x+2=0$

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 

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

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

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

State whether the given equation is quadratic or not. Give reason. 

$\frac{5}{4}{m}^2-7=0$

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

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

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

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

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

A motorboat whose speed is $18 \mathrm{km}/\mathrm{h}$ in still water takes $1$ hour more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. Find the speed of the stream.