Review question

# How many real roots does $(x-1)(x+2)(x+3)=3x$ have? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7792

## Question

Express $\dfrac{3x}{(x-1)(x+2)}$ in partial fractions.

Show that $\dfrac{dy}{dx}$ is negative at all points on the graph of $y=\frac{3x}{(x-1)(x+2)}.$

Sketch this graph, showing the two asymptotes parallel to the $y$-axis and the asymptote perpendicular to the $y$-axis.

By sketching on the same diagram a second graph (the equation of which should be stated), or otherwise, find the number of real roots of the equation $(x-1)(x+2)(x+3)=3x.$