How do you find a fifth degree polynomial

Fifth Degree Polynomials

One to five roots.

Zero to four extrema.

One to three inflection points.

No general symmetry.

It takes six points or six pieces of information to describe a quintic function.

Roots are not solvable by radicals (a fact established by Abel in 1820 and expanded upon by Galois in 1832)

Step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: