Question

What are the possible number of positive real, negative real, and complex zeros of
f(x) = 6x3 - 3x2 + 5x + 9?

Answer 1

Positive Real: 1
Negative Real: 0
Complex: 2

Positive Real: 1
Negative Real: 2 or 0
Complex: 2 or 0

Positive Real: 2 or 0
Negative Real: 1
Complex: 2 or 0

Positive Real: 2 or 0
Negative Real: 2 or 0
Complex: 1

Answer 2

Positive Real: 2 or 0
Negative Real: 1
Complex: 2 or 0

Refer to the plot attached.
The real root is the following to 6 significant digits.\[x=-0.800375 \]

Answer 3

Thanks!