........ also mentioned a method to find the solution of quadratic equation.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0, x=-\sqrt{2}$

Examine whether the following equation is quadratic or not: $(x-3)(2x+1) = x(x+5)$

If one of the roots of the equation $x^{2}-(1+k)x+\sqrt{2}=0$ is $\sqrt{2},$ then find $k$.

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.

$A$ train travels at a certain average speed for a distance of $63 \, km$ and then travels a distance of $72 \, km$ at an average speed of $6 \, km/h$ more than its original speed. If it takes $3 \, hours$ to complete the total journey,what is its original average speed in $km/h$?