Answer:
The roots are [tex]x=-8i[/tex] or [tex]x=8i[/tex]
Step-by-step explanation:
The given polynomial is [tex]f(x)=2x^2+128[/tex]
To find the roots, we equate the polynomial to zero and solve for x.
tex]\implies 2x^2+128=0[/tex]
tex]\implies 2x^2=-128[/tex]
Divide through by 2
[tex]\implies x^2=-64[/tex]
Take square root of both sides
[tex]\implies x=\pm\sqrt{-64}[/tex]
This gives us:
[tex]\implies x=\pm8i[/tex]
The roots are [tex]x=-8i[/tex] or [tex]x=8i[/tex]
