discuss the nature of the zeros of f(x)=x^2+4x+5

Question

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Answer 1

The zeroes are complex.

Complete the square: x^2+4x+4+1 has zeroes when x^2+4x+4=-1 or (x+2)^2=-1. Take square roots of each side:

x+2=±i where i is the imaginary square root of -1. Therefore x=i-2 or -i-2. Imaginary zeroes can be represented as points in a Cartesian plane, in this case (-2,1) and (-2,-1) where the x coord is the real part (-2) and the y coord is the imaginary part (1 or -1, the coefficient of i).