The zeros of P(x)=x^2+16

Question

x₁ = __+(-4) i negative imaginary part,
its multiplicity is ____;

And

x₂ =___+(4) i with positive imaginary part,
its multiplicity is___.

Answer 1

Set P(x) equal to zero to find all zeros.

 

x² + 16 = 0

 

x² = -16

 

x = ± √(-16)

 

x₁ = -4i

x₂ = 4i

 

If we set the two roots as a factor equal to zero, we will see its multiplicity value.

 

(x₁ + 4i)(x₂ - 4i) = 0

 

Each root has a multiplicity of 1 because each of the roots only appear one time.