R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: Exercise 4C

Find the discriminant of the equation $\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0$.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

$\frac{1}{x}-\frac{1}{x-2}=3, x\ne 0, 2$

If $\alpha$ and $\beta$ are the roots of the equation, then find  $\sqrt{3}\left|\alpha -\beta \right|$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$\frac{m}{n}{x}^2+\frac{n}{m}=1-2x$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2-2ax+\left(a^2-b^2\right)=0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2+6x-\left(a^2+2a-8\right)=0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2+5x-\left(a^2+a-6\right)=0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$4x^2-4a^{2}x+\left(a^4-b^4\right)=0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$4x^2+4bx-\left(a^2-b^2\right)=0$