Find All Real Zeros of the Polynomial $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

question 124

Essay

Find all real zeros of the polynomial $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$ . Sketch the graph of $p$ .

---

Definitions:

Whirls

Circular or spiraling patterns or movements.

Euglenoid

Refers to single-celled organisms within the kingdom Protista, characterized by their ability to be both autotrophic and heterotrophic.

Elaborate Shells

Complex and intricately designed outer coverings that protect the bodies of certain animals, like snails and turtles.

Silica

A hard, unreactive chemical compound of silicon and oxygen, used in various industries and forming the major constituent of sand.