Textbook QuestionDetermine whether each statement is true or false. If false, explain why. A polynomial function having degree 6 and only real coefficients may have no real zeros.437views
Textbook QuestionIn Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x^4−11x^3−3x^2−6x+8183views
Textbook QuestionUse the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 4x^2+2x+54; x-4354views
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+2x^2+3; x-1393views
Textbook QuestionFactor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^3-3x^2-5x+6; k=1316views
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=4; -2, 5, and 3+2i are zeros; f(1) = -96335views
Textbook QuestionIn Exercises 33–38, use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=x^3+2x^2+5x+4214views
Textbook QuestionFor each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3+4x^2-5; 1270views
Textbook QuestionIn Exercises 37–38, use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x) = 3x^4 - 2x^3 - 8x + 5252views
Textbook QuestionSolve each problem. Find a polynomial function ƒ of degree 3 with -2, 1, and 4 as zeros, and ƒ(2)=16.417views
Textbook QuestionIn Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. g(x) = x^4 - 6x^3 + x^2 + 24x + 16239views
Textbook QuestionFor each polynomial function, find all zeros and their multiplicities. ƒ(x)=5x^2(x^2-16)(x+5)308views
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. 2x^5+7x^4−18x^2−8x+8=0295views
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. 2-i, 3, and -1163views
Textbook QuestionExercises 82–84 will help you prepare for the material covered in the next section. Solve: x^2+4x+6=0161views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=5x^4+3x^2+2x-9159views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=2x^5-x^4+x^3-x^2+x+5191views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=-2x^5+10x^4-6x^3+8x^2-x+1323views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^5-6x^4+14x^3-20x^2+24x-16394views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=2x^4-x^3+7x^2-4x-4129views