3 Find all real zeros of the function fx x3x2 16x16 Soluti

3. Find all real zero(s) of the function f(x) = x3-x2 + 16x-16

Solution

f(x) = x³-x²+16x-16

f(x)= x²(x-1)+16(x-1) =(x²+16)(x-1)

TO find the zeroes we have to set f(x)=0

(x²+16)(x-1)=0

x^2 +16=0 , x-1=0

x^2=-16, x=1

x=-4i, 4i,1

So the only real zero is x=1