Sec3.3#61 57–62 - Factor Theorem Show that the given value(s) of c arezeros of P(x), and find all other zeros of P(x).57. P(x) = x³ + 2x? – 9xc = -218,58. Р(x) -x3 – 5x? – 2x + 10,c = 5|59. P(x) = x³ – x² – 11x + 15, c = 3||60. P(x) = 3xª – x³ – 21x? – 11x + 6,– 2,c =|61. Р(х)3x8x314x? + 31x + 6,с 3D —2, 3-62. Р(х)2x4 – 13x3 + 7x² + 37x + 15, c = -1, 3

Name: Sec3.3#61 57–62 - Factor Theorem Show that the given value(s) of c are
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Sec3.3#61 57–62 - Factor Theorem Show that the given value(s) of c arezeros of P(x), and find all other zeros of P(x).57. P(x) = x³ + 2x? – 9xc = -218,58. Р(x) -x3 – 5x? – 2x + 10,c = 5|59. P(x) = x³ – x² – 11x + 15, c = 3||60. P(x) = 3xª – x³ – 21x?

Answered: Image /qna-images/answer/9ae68fa9-17e9-4d66-a9e4-230963f090a7.jpg

Answered: 57. P(x) = x³ + 2x² – 9x – 18, c = -2

Math

Algebra

57. P(x) = x³ + 2x² – 9x – 18, c = -2

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra

Problem 4E

See similar textbooks

Similar questions

The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
1. If the result of a polynomial division is 2x3 − 4x2 − 5x + 23 x + 2, make at least three definitive statements about the dividend and the divisor that is involved. 2. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4 x − 2 are the same in every respect. Provide evidence to support your position. 3. Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts. Provide evidence to support your position.
Show that the cubic polynomial p(x) = ax3 + bx2 + cx + d has exactly one point of inflection (x0, y0), where value of x0 and y0 is attached. Use these formulas to find the point of inflection of p(x) = x3 − 3x2 + 2.
6. A polynomial, p(x)=3x^4+Bx^3+Cx^2+x-2, has real coefficients. a. Show that P(x) has at least one positive and one negative real zero. b. Given that one of the zeros of P(x) is -4/3, what can we say for certain about B(the x^3 coefficient) and C (the x^2 coefficient?
Suppose that Rx is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that Rx has the following zeros. 2, 5-3i, -i Answer the following. (a) Find another zero of Rx . (b) What is the maximum number of real zeros that Rx can have? (c) What is the maximum number of nonreal zeros that Rx can have?
Suppose that R(x) is a polynomial of degree 7. Coefficient are real numbers 2-5i, -1+3i, 2i A) Find another zero of r(x) B) what is the maximum number of zeros that R(x) can have? C) what is maximum number of numbers zero that r(x) can have?
If the result of a polynomial division is 2x3 − 4x2 − 5x +23x + 2, make at least threedefinitive statements about the ???????? and the ??????? that is involved. Do you agree with the contention that the functions f(x) = x + 2 and g(x) =x2 − 4x − 2are the same in every respect. Provide evidence to support your position. Do you agree with the statement that “ cubic functions must have at least 1x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts.Provide evidence to support your position.
Which of the following statements are true regarding thegraph of the cubic polynomial f1x2 = x3 + bx2 + cx + d?(Give reasons for your conclusions.)(a) It intersects the y-axis in one and only one point.(b) It intersects the x-axis in at most three points. (c) It intersects the x-axis at least once.(d) For x very large, it behaves like the graph of y = x3. (e) It is symmetric with respect to the origin.(f) It passes through the origin.
A quartic polynomial P(x) has rational coefficients. If √2 and 1 + i are roots of P(x) = 0, what are the two other roots?
3. Given the polynomial function y = A x^3 + 6x^2- Bx , where A and B are unknown constants. If possible, determine the values of A and B so that the graph of y has a maximum value at x= -1 and an inflection point at x=1 .
1 ) Find the cubic polynomial function f(x) with real coefficient that has 2, and 1-i as zero and f(1)=3 2 ) Find the quartic ( fourth degree) polynomial function f with real coefficients that has 1,-2 and 2i as zeros and f(-1)=10 3) Find the cubic polynomial function f(x) with real coefficient that has 2, and 1-i as zero and f(1)=6 4 ) Find the quartic ( fourth degree) polynomial function f with real coefficients that has 1,-2 and 2i as zeros and f(-1)=20
3. Find all zeros of x3+2x2−5x−6 given x=2 is a zero.