Review question

# When does $x^4=(x-c)^2$ have four real roots? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9546

## Suggestion

Given a real constant, $c$, the equation $x^4=(x-c)^2$ has four real solutions (including possible repeated roots) for

1. $c\leq \frac{1}{4}$,
2. $-\frac{1}{4} \leq c \leq \frac{1}{4}$,
3. $c \leq -\frac{1}{4}$,
4. all values of $c$.

Remember that there are two possible solutions when we solve an equation of the form $y^2=a$.
The blue curve is $y = x^4 - (x-c)^2$.