Decartes Rule of Signs Leave a Comment / By doina@highschoolmathtests.com / March 1, 2023 March 1, 2023 1. What are the possible numbers of positive real, negative real, and complex zeros of \[f(x)=7 x^{3}-2 x^{2}+5 x+3\] 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 2. What are the possible numbers of positive real, negative real, and complex zeros of \[f(x)=5 x^{3}+x^{2}+9 x-10\] 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 3. What are the possible numbers of positive real, negative real, and complex zeros of \[f(x)=-7 x^{4}-12 x^{3}+9 x^{2}-17 x+3\] Positive Real: 3 or 1; Negative Real: 1; Complex: 2 or 0 Positive Real: 3 or 1; Negative Real: 2 or 0; Complex: 1 Positive Real: 1; Negative Real: 3 or 1; Complex: 2 or 0 Positive Real: 4, 2 or 0; Negative Real: 1; Complex: 0 or 1 or 3 4. What are the possible numbers of positive real, negative real, and complex zeros of \[f(x)=6 x^{4}+11 x^{3}-7 x^{2}+x+5\] Positive Real: 1; Negative Real: 3 or 1; Complex: 2 or 0 Positive Real: 2 or 0; Negative Real: 0; Complex: 2 or 4 Positive Real: 3 or 1; Negative Real: 1; Complex: 2 or 0 Positive Real: 2 or 0; Negative Real: 2 or 0; Complex: 4, 2 or 0 5. What are the possible numbers of positive real, negative real, and complex zeros of \[f(x)=2 x^{3}- x^{2}+ x+3\] Positive Real: 1; Negative Real: 0 ; Complex: 2 Positive Real: 2 or 0; Negative Real: 1; Complex: 2 or 0 Positive Real: 1; Negative Real: 2; or 0 Complex: 2 or 0 Positive Real: 2 or 0; Negative Real: 2 or 0; Complex: 1 1 out of 5 Time's upTime is Up!