R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 4A

Show that $x=-\frac{bc}{ad}$ is a solution of the quadratic equation $a{d}^2\left(\frac{ax}{b}+\frac{2c}{d}\right)x+b{c}^2=0$

Solve each of the following quadratic equations:

$\frac{x}{x+1}+\frac{x+1}{x}=2\frac{4}{15}, x\ne 0, -1$

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

Solve each of the following quadratic equations:

$\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}, x\ne 2, 4$

If $\alpha$ and $\frac{\alpha }{2}$ are the roots of the equation, then find $\alpha$

Solve each of the following quadratic equations:

$\frac{1}{x+1}+\frac{2}{x+2}=\frac{5}{x+4}, x\ne -1, -2, -4$

If $\alpha$ and $\frac{-3}{\alpha }$ are the roots of the equation, then find $\alpha$

Solve each of the following quadratic equations:

$\frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4}, x\ne -1, -\frac{1}{5}, -4$

If $\alpha$ and $-\frac{\left(10+\alpha \right)}{17}$ are the roots of the equation, then find $\alpha$

Solve each of the following quadratic equations:

$\frac{a}{(ax-1)}+\frac{b}{(bx-1)}=(a+b), \left(x\ne \frac{1}{a}, \frac{1}{b}\right)$

If the product of roots is $\frac{k}{ab}$, then find the value of $k$?

Solve each of the following quadratic equations:

$3^{(x+2)}+3^{-x}=10$

If $a$ and $b$ are the roots of the equation then find $(a-b{)}^2$?

Solve each of the following quadratic equations:

$4^{(x+1)}+4^{(1-x)}=10$

If $a$ and $b$ are the roots of the equation then, find $(a-b{)}^2$