Chapter 5 Polynomials and Polynomial Functions - 5.6 Find Rational Zeroes - 5.6 Exercises - Skill Practice - Page 375: 38

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Given: $f(x)=2x^4-5x^3+10x^2-9$ The leading coefficient is $\pm 1,\pm 2, \pm 4$ The constant term is $\pm 1,\pm3$ The possible rational zeros are: $\pm \frac{1}{1},\pm \frac{3}{1},\pm \frac{1}{2},\pm \frac{3}{2},\pm \frac{1}{4},\pm \frac{3}{4}$ Hence, there are $12$ possible rational zeros.