Textbook QuestionDetermine whether each statement is true or false. If false, explain why. For ƒ(x)=(x+2)^4(x-3), the number 2 is a zero of multiplicity 4.259views1rank
Textbook QuestionIn Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=4x^4−x^3+5x^2−2x−6225views
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+6x^2-2x-7; x+1145views
Textbook QuestionIf ƒ(x) is a polynomial function with real coefficients, and if 7+2i is a zero of the function, then what other complex number must also be a zero?250views
Textbook QuestionIn 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; -5 and 4+3i are zeros; f(2) = 911740views1rank
Textbook QuestionShow 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 less than -3165views
Textbook QuestionFor each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3-x^2-4x-6; 3274views
Textbook QuestionSolve each problem. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x)=x^3+3x^2-4x-2.299views
Textbook QuestionIn Exercises 35–36, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x) = x^4 - 6x^3 + 14x^2 -14x + 5576views
Textbook QuestionIn Exercises 39–52, find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. f(x)=3x^4−11x^3−x^2+19x+6662views
Textbook QuestionIn Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. f(x) = 2x^4 + 3x^3 + 3x - 2323views
Textbook QuestionFor each polynomial function, find all zeros and their multiplicities. ƒ(x)=3x(x-2)(x+3)(x^2-1)257views
Textbook QuestionExercises 53–60 show incomplete graphs of given polynomial functions. a) Find all the zeros of each function. b) Without using a graphing utility, draw a complete graph of the function. f(x)=3x^5+2x^4−15x^3−10x^2+12x+8201views
Textbook QuestionFind a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. See Examples 4–6. 5+i and 5-i548views
Textbook QuestionExercises 82–84 will help you prepare for the material covered in the next section. Solve: x^2+4x−1=0189views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=3x^3+6x^2+x+7177views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=x^5+3x^4-x^3+2x+3158views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=9x^6-7x^4+8x^2+x+6143views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=7x^5+6x^4+2x^3+9x^2+x+5234views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=2x^5+11x^4+16x^3+15x^2+36x485views