Question

Find the zeros of x raised to 3 + 1

Answer 1

x³ + 1 = 0

use formula,
a³ + b³ = (a + b)( a² -ab + b²)

so,
x³ + 1 = (x +1)( x² -x +1) =0

hence , x + 1 =0 and x² -x +1 =0
x = -1 and x² -x +1 =0

for x² -x +1 =0
find Discriminant = b² -4ac = (-1)² -4 <0
so, no real roots possible , hence, we use conplex number concept for solving this .
now,
x² - x +1 =0

x² -x = -1

x² -x +(1/2)² = (1/2)² -1 = -3/4

(x -1/2)² = (-3/4)

take square root both sides

(x -1/2) = ±√3i/2

x = 1/2 ± √3i/2

x = (1±√3i)/2

hence, roots of x³ +1 is -1, (1+√3i)/2 , and (1-√3i)/2

Answer 2

x^3+1=0

x^3=-1

x=-1

I hope this will help u ;)