Quadratic Equations

Given $x+y=11$ and $xy=20$. What is the value of $(x-y)?$

How many of the following values of $x$ would satisfy the equation $q{x}^2-2px+q=0$?

$1$. $x=\frac{\sqrt{p+q}+\sqrt{p-q}}{\sqrt{p+q-\sqrt{p-q}}}$, where $p>q$

$2$. $x=\frac{p+\sqrt{p^2-q^2}}{q}$, where $p>q$

$3$. $x=\frac{\sqrt{p+q}}{\sqrt{p-q}}$, where $p>q$

Select the correct answer using the code given below:

The number of zeroes of $0x^2+x-1$ is/are

If $\alpha$ and $\beta$ are the roots of the equation $x^2-4x+1=0$ the value of ${\alpha }^3+{\beta }^3$ is

Amal and his family went for a trip to a resort. There are various amenities in the resort. He went for boating in the stream nearby the resort. The 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.

Solve the following equations and find the answer.
I. $4X^2-13X-12=0$

II. $Y^2-7Y-60=0$

If $x^2+1-2x=0,x>0$, then $x^2\left(x^2-2\right)$ ______.

The roots of the quadratic equation $4x^2-5x-3=0$ when corrected to two decimal places are: $\left(\sqrt{73}=8.544\right)$

It is being given that one of the roots is half the sum of the other two solving $x^3-12x^2+47x-60=0$ we get the following roots _____.

The equation $\left(\frac{l-m}{2}\right)x^2-\left(\frac{l+m}{2}\right)x+m=0$ has  got two values of x to satisfy the equation given as _____.

The solutions of the equation $\frac{6x}{x+1}+\frac{6(x+1)}{x}=13$ are ______.

If $\alpha$ and $\beta$ are the sum and the product of the roots of the quadratic equation $4$$x^2$ $+\left(12+20\sqrt{2}\right)x +60\sqrt{2} =0$,Then find $\alpha +\beta$

The solution of $2x^2-5x+3=0$ is

The roots of the quadratic equation $3q^2–2q=8$ are

Solve for $x$: $3x^2+5x-9=0$. Give your positive answer correct to two decimal place.

The speed of a boat in still water is $7\mathrm{km}/\mathrm{hr}$. It can go $24\mathrm{km}$ downstream and $8\mathrm{km}$  upstream in$6 hours$. Find the speed of the stream.

Find the value of $k$ for which the following equation has equal roots $x^2+4kx+\left(k^2-k+2\right)=0$

Solve using the quadratic formula $x^2-4x+1=0$

By solving this $4\left(x^2+\frac{1}{x^2}\right)+8\left(x-\frac{1}{x}\right)-29=0$, we get one of the root as $\frac{-1}{2}$, then find the other root. 

Solve the following equations correct to two decimal places using formula only.

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