Review question

# Can we show this quartic equation has 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: R7549

## Question

Sketch in the same diagram the graphs of $y = x^2$ and $x^2 + y^2 - 4x + 2y - 4 = 0$. Hence or otherwise show that the equation $x^4 + 3x^2 - 4x - 4 = 0$ has two and only two real roots.

Find the positive root of the equation correct to one decimal place.