Solutions
Solutions to Try Its
1. [latex]f\left(-3\right)=-412[/latex] 2. The zeros are 2, –2, and –4. 3. There are no rational zeros. 4. The zeros are [latex]\text{-4, }\frac{1}{2},\text{ and 1}\text{.}[/latex] 5. [latex]f\left(x\right)=-\frac{1}{2}{x}^{3}+\frac{5}{2}{x}^{2}-2x+10[/latex] 6. There must be 4, 2, or 0 positive real roots and 0 negative real roots. The graph shows that there are 2 positive real zeros and 0 negative real zeros. 7. 3 meters by 4 meters by 7 metersSolutions to Odd-Numbered Exercises
1. The theorem can be used to evaluate a polynomial. 3. Rational zeros can be expressed as fractions whereas real zeros include irrational numbers. 5. Polynomial functions can have repeated zeros, so the fact that number is a zero doesn’t preclude it being a zero again. 7. –106 9. 0 11. 255 13. –1 15. –2, 1, [latex]\frac{1}{2}[/latex] 17. –2 19. –3 21. [latex]-\frac{5}{2}, \sqrt{6}, -\sqrt{6}[/latex] 23. [latex]2, -4, -\frac{3}{2}[/latex] 25. 4, –4, –5 27. [latex]5, -3, -\frac{1}{2}[/latex] 29. [latex]\frac{1}{2}, \frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}[/latex] 31. [latex]\frac{3}{2}[/latex] 33. 2, 3, –1, –2 35. [latex]\frac{1}{2}, -\frac{1}{2}, 2, -3[/latex] 37. [latex]-1, -1, \sqrt{5}, -\sqrt{5}[/latex] 39. [latex]-\frac{3}{4}, -\frac{1}{2}[/latex] 41. [latex]2, 3+2i, 3 - 2i[/latex] 43. [latex]-\frac{2}{3}, 1+2i, 1 - 2i[/latex] 45. [latex]-\frac{1}{2}, 1+4i, 1 - 4i[/latex] 47. 1 positive, 1 negative![Graph of f(x)=x^4-x^2-1.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201604/CNX_PreCalc_Figure_03_06_202.jpg)
![Graph of f(x)=x^3-2x^2+x-1.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201605/CNX_PreCalc_Figure_03_06_204.jpg)
![Graph of f(x)=2x^3+37x^2+200x+300.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201608/CNX_PreCalc_Figure_03_06_206.jpg)
![Graph of f(x)=2x^4-5x^3-5x^2+5x+3.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201610/CNX_PreCalc_Figure_03_06_208.jpg)
![Graph of f(x)=10x^4-21x^2+11.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201611/CNX_PreCalc_Figure_03_06_210.jpg)