Given function
.
The coefficient of
is 1,there 4, 2, 0 are pisitive real roots and 0 nagative real roots.
The possible rational zeros are
.
| \
x \ | \
\
1 \ | \
\
| \
\
| \
\
| \
\
| \
| \
1 \ | \
\
1 \ | \
\
0 \ | \
\
| \
\
| \
\
| \
| \
| \
\
1 \ | \
2 | \
\
1 \ | \
\
| \
\
0 \ | \
| \
| \
\
1 \ | \
\
| \
\
5 \ | \
11 | \
\
20 \ | \
| \
3 \ | \
\
1 \ | \
\
2 \ | \
\
5 \ | \
42 | \40 | \
One zero is
1.
(Substitute f(x) = 0)

(Apply distributive property)
(Set 1st factor on equal to zero)
(Subtract 1 from each side)

(The imaginary value:
)
(Set second factor on equal to zero)
(Add 2 to each side)
(Simplify)
(Add)
Here another real zero at x = 2, two imaginary zeros at
.
The zeros of this function are
.