R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 5: EXERCISE 4.5

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

$3x^2-5x+2=0$

If the roots are $1 \text{and} \frac{k}{3}$, find $k$.

Solve for $x$, 

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

If the value of $x$ are $k \mathrm{and} \frac{k}{2}$, find $k$.

Solve for $x:$

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

Solve for $x$:

 $x+\frac{1}{x}=3, x\ne 0$

If $x$ is $\frac{3\pm \sqrt{k}}{2}$, find $k$.

Solve for $x$, 

$\frac{16}{x}-1=\frac{15}{x+1}, x\ne 0, -1$

If $x$ is $\pm k$, find $k$.

Solve for $x.$

$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6},x\ne 3,-5$

Determine the nature of the roots of the following quadratic equation:

$\frac{3}{5}{x}^2-\frac{2}{3}x+1=0$

Determine the nature of the roots of the following quadratic equation: 

$3x^2-4\sqrt{3}x+4=0$