Review question

# Can we find the repeated root for $4x^4+x^2+3x+1=0$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9082

## Suggestion

Prove that, if $\alpha$ is a repeated root of $f(x)=0$, where $f(x)$ is a polynomial, then $\alpha$ is a root of the equation $f'(x)=0$.

If $f$ has a repeated root at $\alpha$, how can we write $f$? Can we now differentiate?

Given that the equation $4x^4+x^2+3x+1=0$ has a repeated root, find its value.

Can we apply the first part of the question, together with the Factor Theorem?