Textbook Question
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x4−11x3−x2+19x+6
361
views
4. Polynomial Functions
Zeros of Polynomial Functions
Back4. Polynomial Functions
Zeros of Polynomial Functions
- Textbook QuestionUse the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. x^3-5x^2+3x+1; x-1224views
- Textbook Question
In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x3−3x2−11x+6
282views - Textbook QuestionShow that f(x) = x^3 - 2x - 1 has a real zero between 1 and 2.502views
- Textbook Question
In Exercises 25–32, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 1 and 5i are zeros; f(-1) = -104
539views - Textbook Question
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x^3-37x^2+50x+60 Find the zero in part (b) to three decimal places.
232views - Textbook QuestionFactor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^4+x^3-9x^2-13x-5; k=-1 (multiplicity 3)304views
- Textbook Question
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5 no zero greater than 1
311views - Textbook Question
In Exercises 47–48, find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3; 2 and 2 - 3i are zeros; f(1) = -10
971views - Textbook QuestionFor each polynomial function, find all zeros and their multiplicities. ƒ(x)=(x+1)^2(x-1)^3(x^2-10)304views
- Textbook QuestionFind a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. See Example 4. Zeros of -2, 1, and 0; ƒ(-1)=-1298views
- Textbook QuestionFind a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. See Example 4.Zero of -3 having multiplicity 3; ƒ(3)=36425views
- Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=4x^3-x^2+2x-7250views
- Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=6x^4+2x^3+9x^2+x+5289views
- Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=5x^6-6x^5+7x^3-4x^2+x+2263views