Review question

# When does $3x^4-16x^3+18x^2=k$ have exactly two real roots? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6537

## Suggestion

Find the coordinates of each turning point on the graph of $y=3x^4-16x^3+18x^2$ and determine in each case whether it is a maximum point or a minimum point.

How can we determine if a turning point is a minimum or a maximum?

Sketch the graph of $y=3x^4-16x^3+18x^2$, and state the set of values of $k$ for which the equation $3x^4-16x^3+18x^2=k$ has precisely two real roots for $x$.

What does the line $y=k$ look like on the graph?

We could try using a ruler as $y=k$, and explore what happens when we add this to the graph of $y=3x^4-16x^3+18x^2$ as we vary $k$.