Textbook QuestionIn Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=x^3+x^2−4x−4293views
Textbook QuestionDetermine whether each statement is true or false. If false, explain why. The product of a complex number and its conjugate is always a real number.232views
Textbook QuestionIn 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)=x^3+x^2−4x−4296views
Textbook QuestionIn 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)=x^3−2x^2−11x+12552views
Textbook QuestionIn 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)=2x^3+x^2−3x+1341views
Textbook QuestionIn Exercises 16–17, find the zeros for each polynomial function and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x) = -2(x - 1)(x + 2)^2(x+5)^2440views
Textbook QuestionIn Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. x^3−10x−12=0437views
Textbook QuestionUse the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 2x^4+5x^3-2x^2+5x+6; x+3300views
Textbook QuestionFind a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. √3, -√3, 2, 3272views
Textbook QuestionFind a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. -2+√5, -2-√5, -2, 1137views
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; i and 3i are zeros; f(-1) = 20456views
Textbook QuestionFactor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=x^4+2x^3-7x^2-20x-12; k=-2 (multiplicity 2)582views
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)=3x^3-8x^2+x+2 between -1 and 0123views
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)=3x^3-8x^2+x+2 between 2 and 3137views
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)=3x^3-8x^2+x+2 Find the zero in part (b) to three decimal places.174views
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)=4x^3-37x^2+50x+60 between 7 and 8258views
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)=4x^3-37x^2+50x+60 between 2 and 3141views
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)=2x^4−5x^3−x^2−6x+4448views
Textbook QuestionFor each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=-x^4-5x^2-4; -i401views
Textbook QuestionFor Exercises 40–46, (a) List all possible rational roots or rational zeros. (b) Use Descartes's Rule of Signs to determine the possible number of positive and negative real roots or real zeros. (c) Use synthetic division to test the possible rational roots or zeros and find an actual root or zero. (d) Use the quotient from part (c) to find all the remaining roots or zeros. f(x) = x^3 + 3x^2 - 4448views
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)=x^4−2x^3+x^2+12x+8249views
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. 4x^4−x^3+5x^2−2x−6=0405views
Textbook QuestionFor each polynomial function, find all zeros and their multiplicities. ƒ(x)=(2x^2-7x+3)^3(x-2-√5)435views
Textbook QuestionFind a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. See Example 4. Zeros of -3, 1, and 4; ƒ(2)=30429views
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)=4x^3−8x^2−3x+9194views
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 QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=x^3+2x^2+x-10251views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=-8x^4+3x^3-6x^2+5x-7160views
Textbook QuestionDetermine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=11x^5-x^3+7x-5175views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4+2x^3-3x^2+24x-180164views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4+4x^3+6x^2+4x+1402views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4+2x^2+1124views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4-6x^3+7x^2132views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4-8x^3+29x^2-66x+72232views
Textbook QuestionFind all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^6-9x^4-16x^2+144163views