The necessary condition for $ax^2 + bx + c = 0$,where $a, b, c \in R$,to be a quadratic equation is:

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

$A$ car takes $60$ minutes less for a journey of $150\,km$,if its speed is increased by $5\,km/hr$ from its usual speed. Find the original speed of the car in $km/hr$.

Solve the following equation using the method of factorization and write its solution set: $x + 2 - \frac{6}{x + 2} = 1$

Every quadratic polynomial has at the most ......... zero/s.

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