Question

Solve x^3+3x^2-23x-20=0

Answer 1

Hello from MrBillDoesMath!

Answer:

x = 4

x  =  ( -7 + sqrt(29)) /2

x =   ( -7 - sqrt(29)) /2

Discussion:

x^3+3x^2-23x-20 factors as (x - 4) (x^2 + 7 x + 5) so x =4 is one root

The roots of the quadratic factor, x^2 + 7x + 5, can be found using the quadratic formula where a = 1, b = 7, and c = 5

x =  (  -b +\- sqrt(b^2-4ac)) / 2a

x = ( -7 +\- sqrt( 7^2 - 4*1*5) ) / (2*1) =>

x =  ( -7 +\- sqrt (49-20) ) /  2 =>

The "+" root:    ( -7 + sqrt(29)) /2

The "-" root:    ( -7 - sqrt(29)) /2

Regards,  

MrB