Review question

# Can we show $(x^2+1)(x+1)=(a^2+1)(a+1)$ has just one real root? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9108

## Suggestion

Prove that, if $a$ is real, the equation $(x^2+1)(x+1)=(a^2+1)(a+1)$ has one and only one real root.

Can we identify one obvious root of this equation?

Could we then factorise to find any other possible roots?