Practice variation 3 of 3
Polynomial roots — Original curves, full chain
Your question
Consider and , .
(i) Show that intersection -coordinates satisfy .
(ii) Hence, by imposing a repeated root of , find the exact value of for a single intersection point.
This practice question was inspired by Question 14(b) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?