The roots of the quadratic equation $4x^{2} + 4x - 3 = 0$ are

Obtain the roots of the following quadratic equation by using the general formula for the solution: $25x^2 + 20x + 7 = 0$.

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

State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}+5x+5=0$

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $2x^2 - 2\sqrt{2}x + 1 = 0$.