Question 1090923


{{{y = x^3 - x^2 - 4x +7 }}} where {{{a=1}}},{{{b=-1}}},{{{c=-4}}}, and {{{d=7}}}

use this formula:

{{{x=root(3,(-b^3/(27a^3)+bc/6a^2-d/2a)+sqrt((-b^3/(27a^3)+bc/6a^2-d/2a)^2+(c/3a-b^2/9a^2)^3) )+root(3,(-b^3/(27a^3)+bc/6a^2-d/2a)-sqrt((-b^3/(27a^3)+bc/6a^2-d/2a)^2+(c/3a-b^2/9a^2)^3) ) -b/3a}}}

or

{{{x   =   (q + (q^2 + (r-p^2)3)^(1/2))^(1/3)   +   (q - (q^2 + (r-p^2)^3)^(1/2))^(1/3)   +   p}}}

 where
{{{p = -b/(3a)}}},   
{{{q = p^3 + (bc-3ad)/(6a^2)}}},   
{{{r = c/(3a)}}}

and you will get:

 {{{x=-2.22}}}

{{{x=1.61 + i* 0.75}}}

{{{x=1.61 - i* 0.75}}}