Question 937988
By definition, "complex zeros" involves imaginary numbers.
.
f(x)=x²+2x+3
since we can't factor the right side we apply the "quadratic equation":
x = (-b +- sqrt(b^2 - 4ac))/(2a)
x = (-2 +- sqrt(2^2 - 4(1)(3)))/(2(1))
x = (-2 +- sqrt(4 - 12))/2
x = (-2 +- sqrt(-8))/2
x = (-2 +- sqrt(-2*2*3))/2
x = (-2 +- 2sqrt(-3))/2
x = (-2 +- 2isqrt(3))/2
x = -1 +- sqrt(3)i
.
there are two complex roots:
x = -1-sqrt(3)i
and
x = -1+sqrt(3)i