select the correct answer from the drop - down menu. the values $x = 2pm i$ are the roots of the quadratic…

select the correct answer from the drop - down menu. the values $x = 2pm i$ are the roots of the quadratic equation

select the correct answer from the drop - down menu. the values $x = 2pm i$ are the roots of the quadratic equation

Answer

Explanation:

Step1: Recall the formula for quadratic equation from roots

If the roots of a quadratic equation are (x = r_1) and (x = r_2), the quadratic equation is ((x - r_1)(x - r_2)=0). Here (r_1=2 + i) and (r_2=2 - i).

Step2: Expand ((x-(2 + i))(x-(2 - i)))

[ \begin{align*} &(x-(2 + i))(x-(2 - i))\ =&x^2-(2 - i)x-(2 + i)x+(2 + i)(2 - i)\ =&x^2-(2 - i+2 + i)x+(4 - i^2)\ =&x^2-4x+(4+ 1)\ =&x^2-4x + 5 \end{align*} ]

Answer:

(x^{2}-4x + 5=0)