If $-3$ is a solution of $2x^{2} + 5x + k = 0$,then $k = \ldots$

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

Find the roots of the following quadratic equation using the quadratic formula,if they exist: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}$; $(x \neq -1, -2, -4)$

We get $2 \ kg$ of pure butter less in Rs. $960$ if the price of pure butter increases by Rs. $40$ per $kg$. Find the original price of pure butter per kilogram.

Examine whether the following equation is quadratic or not: $x^{2}-3=\frac{2}{x}$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.