Review question

# How many roots does this equation have? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6896

## Question

Sketch the graph of $y = \frac{5x}{x^2 -1},$ showing clearly the three asymptotes.

Use your graph to find the number of real roots of the equation $kx-1 = \frac{5x}{x^2 -1},$ when $k$ is a positive constant.

Show also that there is a range of negative values of $k$ for which the equation has only one real root. (The precise range of values of $k$ is not required.)