If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 24 x + 16 = 0$.

Examine whether the following equation is quadratic or not: $x+\frac{1}{x}=x^{2} (x \neq 0)$

State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

Find the roots of the following quadratic equation by the method of completing the square: $x^{2}+2x-2=0$

While selling a calculator for Rs. $56$,the profit percentage is equal to its cost price in rupees. Find the cost price of the calculator.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.