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

Solve the following equation using the method of factorization: $(x+1)^{2} + x^{2} = 221$.

Write whether the following statements are true or false. Justify your answers.
$(i)$ If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of $x$ term is zero,then the quadratic equation has no real roots.
$(ii)$ Every quadratic equation has at least two roots.

If the value of the discriminant of the quadratic equation $x^{2} + \sqrt{2}x + 2 = 0$ is .... .

If the roots of the quadratic equation $3x^{2} + 2\sqrt{5}x - 5 = 0$ exist,find them using the method of completing the square.

......... can be taken as the value of $k$,if one of the roots of the quadratic equation $k x^{2} - 7x + 6 = 0$ is $\frac{3}{2}$.