Find the discriminant of the following quadratic equation: $x^{2}-7x+10=0$

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

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $\frac{1}{4} x^{2} - 2x + 1 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $2kx^2 - 8x + k = 0$.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} - 3x - 2 = 0$.