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
