Answer
[tex]P(x)=(x^{3}+2x^{2}+25x+50)[/tex]Explanation
Given
• Polynomial function of lowest degree
,• Zeros -2 and 5i
Procedure
The zeros of the polynomial can be written as
[tex]\begin{gathered} x=-2 \\ x+2=0 \end{gathered}[/tex][tex]\begin{gathered} x=5i \\ x-5i=0 \end{gathered}[/tex][tex]\begin{gathered} x=-5i \\ x+5i=0 \end{gathered}[/tex]If we multiply each other we get:
[tex](x+2)(x-5i)(x+5i)=0[/tex]Multiplying the last two factors is the sum of two squares:
[tex](x+2)(x^2+25)=0[/tex]Finally, combining the terms and simplifying:
[tex](x\cdot x^2+2x^2+25x+50)=0[/tex][tex](x^3+2x^2+25x+50)=0[/tex][tex]P(x)=(x^3+2x^2+25x+50)[/tex]