Find all real and imaginary solutions to the polynomial equations by factoring or using the quadratic formula

Question

X^3 - 12=113

Answer 1

x^3 - 12 = 113

 

x^3 - 125 = 0

 

125 = 5^3

 

x^3 - (5)^3 = (x - 5)(x^2 + 5x +25)

 

Roots of x^2 + 5x +25 = 0:

 

r = [-5 ± sqrt(-75)] / 2 = -5/2 ± i (5√3) / 2

 

The thee roots are 5 and -5/2 ± i (5√3) / 2