College Algebra (10th Edition)

The maximum number of real zeros is $3$ The number of positive real zeros is either $2$ or $0$ The number of negative real zeros is $1$
The number of zeros of a polynomial can’t be greater than its degree $1)$ The number of positive real zeros of $f(x)$ either equals the number of variations in the sign of the nonzero coefficients of $f(x)$ or equals that number minus an even integer $2)$ The number of negative real zeros of $f(x)$ either equals the number of variations in the sign of the nonzero coefficients of $f(-x)$ or equals that number minus an even integer. So the maximum number of real zeros here is $3$ Since $$f\left( x\right) =3x^{3}-2x^{2}+x+2$$ has $2$ variations The number of positive real zeros is either $2$ Or $0$ Since $$f\left( -x\right) =-3x^{3}-2x^{2}-x+2$$ Has $1$ variation Number of negative real zeros is $1$