Question

What is Quintic equation ?

Answer 1

$\mathfrak{ \red{quadratic \: equation}}$

$\sf{quadratic \: equation \: is \: an \: equation \: where \: highest \: degree \: is \red{2}}$

$\sf{ \implies{formula \: for \: quadratic \: equation }} \\ \\ a {x}^{2} + bx + c = 0 \\ \\ {\red{abc \: are \: known \: number}} \\ \\ { \red{where \: a \: is \: not \: equal \: to \: 0}} \\ \\ and \: x \: is \: unknown \: number$

it contains at least one term that is squared .

A quadratic equation looks like this when visualized in graph (look at the attached pic)

image source : Google

Answer 2

A Polynomial function equation of the form :

$f(x) = a {x}^{5} + b {x}^{4} + c {x}^{3} + d {x}^{2} + ex + f$

is called a

" General Quintic Polynomial ".

It has exactly five roots, out of which one is the principal real root, i.e., the root which is always supposed to be real if

a ≠ 0, and a,b,c,d,e,f ∈ ℝ

The solutions for the general quintic polynomial are non - algebraic, i.e. Its roots cannot be represented in form of radicals : √ , ∛ , ∜ ,⁵√