Find the zeroes of fx x4 15x2 54Solutionfxx415x254 Let wx

Find the zeroes of f(x) = x^4 + 15x^2 + 54.

Solution

f(x)=x⁴+15x²+54

Let w=x²

therefore f(x)=w²+15w+54

To find the zeroes we need to set f(w)=0

w²+15w+54=0

(w+6)(w+9)=0

w=-6,-9

x²=-6 , x²=-9

x=+-i sqrt6 , +- i 3

Therefore the zeroes are -i sqrt6 ,- 3i, i sqrt6,3i