solve the equaiton exactly in the complex number system.

Question

x^3+3x^2+25x+75=0

Answer 1

We can factor by grouping.

 

x²(x + 3) + 25(x + 3) = 0

 

 

Notice that (x + 3) is the GCF of the left side of equation.

 

(x² + 25)(x + 3) = 0

 

 

Set the factors equal to zero.

 

x² + 25 = 0             and              x + 3 = 0

 

x² = -25                  and               x = -3

 

x = ±√(-25)

 

x = -5i

x = 5i