find all the zeros of fxx43x32x212x24given that x2i is zeroS

find all the zeros of f(x)=x^4-3x^3-2x^2-12x-24,given that x=2i is zero

Solution

for  f(x)=x^4-3x^3-2x^2-12x-24,

given that x=2i is zero

f(2i)=(2i)^4-3(2i)^3-2(2i)^2-12(2i)-24 we know i^2 = -1

f(2i)= (4*{-1})^2 + 24i + 8 -24i - 24

f(2i)= 16 + 24i + 8 -24i - 24

f(2i)= 0

Answer