Write a polynomial equation of degree 2 in standard form given that one root 2 + 5i

x^2 - 4x + 29 = 0

Step-by-step explanation:

Complex roots occur as conjugate pairs.

So the other root will be  2 - 5i.

First write the equation  it in factor form:-

(x - (2 + 5i)) (x - (2 - 5i) = 0

(x - 2 - 5i)(x - 2 + 5i) = 0      Now expand:-

x^2 - 2x + 5ix - 2x + 4 - 10i - 5ix + 10i - 25i^2 = 0

x^2 -2x - 2x + 4 - 25*-1 = 0

x^2 - 4x + 29 = 0   (answer)

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