Question

What is the formula of cubic polynomial

Answer 1

Step-by-step explanation:

$the \: formula \: for \: cubic \: \\ polynomial \: is \geqslant \\ \\ {ax}^{3} + {bx}^{2} + {cx} \: + d$

Answer 2

For any cubic equation of the general form:

ax³+bx²+cx+d = 0

Its three roots are given by the cubic formula:

$x_{1,2,3} = \frac{ - b}{3a} + ω_k \sqrt[3]{ - \frac{ {b}^{3} }{27 {a}^{3} } + \frac{bc}{6 {a}^{2} } - \frac{d}{2a} + \sqrt{( - \frac{ {b}^{3} }{27 {a}^{3} } + \frac{bc}{6 {a}^{2} } - \frac{d}{2a} )^{2} - ( \frac{ {b}^{2} - 3ac}{9 { a}^{2} } }) ^{3} } +({ω_k }^{2}) \sqrt[3]{ - \frac{ {b}^{3} }{27 {a}^{3} } + \frac{bc}{6 {a}^{2} } - \frac{d}{2a} - \sqrt{( - \frac{ {b}^{3} }{27 {a}^{3} } + \frac{bc}{6 {a}^{2} } - \frac{d}{2a} )^{2} - ( \frac{ {b}^{2} - 3ac}{9 { a}^{2} } }) ^{3} }$

Where,

$ω_k = 1 , \frac{-1}{2} ± \frac{i√3}{2}$

where, i = √(–1)