Maths - Quartics

Pearson Edexcel Mathematics 2022

Created: October 11, 2020 | Read markdown | About these notes | View in context | Study these flashcards |

Definition and number of roots

What is a quartic?

quartic-definition

A 4-th degree polynomial.

What’s the largest number of (real) solutions a quartic can have?

quartic-max-real-roots

$4$.

What’s the smallest number of (real) solutions a quartic can have?

quartic-min-real-roots

$0$.

Constructing and sketching quartics

I want to make a quartic with only two roots, $3$ and $4$. How could I do this?

quartic-from-two-repeated-roots
\[(x-3)(x-3)(x-4)(x-4)\]

Visualise the quartic $x^2(x-3)(x+3)$?

visualise-quartic-x-squared-cubic

When sketching a quartic, what’s the process?

quartic-sketching-process
  • Add the roots to an axis
  • Add the y-intercept


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