Quadratic Equat...

The roots of the equation are $$lx^2 + nx+n=0$$ are in the ratio $$p:q$$. Then

$$ (x - a)(x - b) + (x - c)(x - a) + (x - c)(x - b) = 0$$ then its roots are 

Find the roots of the following quadratic equation by using the quadratic formula
$$2x^2 - 2\sqrt 2x + 1 = 0$$

Find the roots of the following quadratic equation by using the quadratic formula
$$\displaystyle x + \frac{1}{x} = 3, x \neq 0$$

Find the roots of the following quadratic equation by using the quadratic formula 
$$x^2 - 16x + 64 = 0$$

Find the roots of the following quadratic equations by using the quadratic formula
$$\displaystyle \frac{x - 3}{x + 3} - \frac{x + 3}{x - 3} = 6\frac{6}{7}, x \neq - 3, 3$$

The discrimiant of the quadratic equation $$\displaystyle 3\sqrt{3}x^{2}+10x+\sqrt{3}=0$$ is 

Find the solutions of $$3x^2 - 2\sqrt 6x + 2 = 0$$ by the method of completing the squares when $$x$$ is a real number.

Let $$\displaystyle \alpha ,\beta $$ and $$\displaystyle \gamma  $$ be the roots of the equation $$( x-1) \displaystyle (x^{2}+x-3)=0.$$ Then, the value of $$\displaystyle (\alpha +\beta )$$ is 

If  $$\displaystyle\alpha, \beta $$ are roots of $$\displaystyle ax^{2}-2bx+c=0$$ then $$\displaystyle a^{3}\beta ^{3}+a^{2}\beta ^{2}+a^{3}\beta^2$$ is