How do you solve?

Question

Create a fourth degree polynomial that has the two roots 2+3i and square root of 5. How do you solve this?

Answer 1

Your 4 roots are

 

x₁ = 2 + 3i

x₂ = 2 - 3i

x₃ = √(5)

x₄ = -√(5)

 

This is because complex numbers have conjugates and square-roots have plus or minus.

 

The roots were obtained by setting the factors of the polynomial to zero.  We will do this in the reverse direction.

 

f(x) = (x - 2 - 3i)) (x - 2 + 3i) (x - √(5)) (x + √(5))