Question

State how many imaginary and real zeros the function has. f(x) = x3 + 5x2 + x + 5

Answer 1

we factor by grouping

f(x)=(x³+x)+(5x^2+5)
f(x)=x(x²+1)+5(x²+1)
undistribute x²+1
f(x)=(x+5)(x²+1)
set each to zero
0=x+5
x=-5

0=x²+1
-1=x²
i=x

1 real root and 1 imaginary root

Answer 2

1 imaginary & 2 reals

Hope I helped! ( Smiles )