use applications of the fundamental theorem of algebra, linear factorizarion theorem, rational zero test 1. f(x)=4x3-9x2-8x-3;...
use applications of the fundamental theorem of
algebra, linear factorizarion theorem, rational zero test
1. f(x)=4x3-9x2-8x-3; x=3
2.g(x)= x3-2x2+9x-18; x=3
Homework Answers
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use applications of the fundamental theorem of
algebra, linear factorizarion theorem, rational zero test
1. f(x)=4x3-9x2-8x-3;...
71 60. 321z+ 61.-2x3 + 5x2-3x+9=0 62. _x3 + 8x-12-0 Use the rational zero theorem, Descartes's...
71
60. 321z+ 61.-2x3 + 5x2-3x+9=0 62. _x3 + 8x-12-0 Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in finding all real and imaginary root 0 to each equation. 一63. x3-4x2-7x+10=0 一64. x3 + 9x2 + 26x + 24 = 0 -65. r3-10x-3=0 66. 2x3-7x2 160 一68. x4-4x3 + 7x2-16x + 12 = 0 69, 6' + 25x2-24x + 5 = 0 70·6x3-11x2-46x-24 0 --71. x4 + 2x3-3x2-4x+4-0 72, x5 + 3x3...
9x2+22x+9 x3+5x2+7x+3 a. Factor the numerator and denominator using the rational zero theorem as needed). Include...
9x2+22x+9 x3+5x2+7x+3 a. Factor the numerator and denominator using the rational zero theorem as needed). Include any factors with irrational zeros but leave quadratic irreducibles as they are (no real zeros) b. State all zeros of f(x) (excluding any complex). c. Determine all asympotes (lines) and any holes (points) if they exist.. d. Write all intercepts as points. Plot all the points and asympotes so far by drawing your own appropriate scale using a ruler. e. Use extra points as...
1. (10 pts.) For the following polynomial; a. Use the Rational Zero Test to list all...
1. (10 pts.) For the following polynomial; a. Use the Rational Zero Test to list all possible rational roots b. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots C. Factor the polynomial completely. x3 + 4x2 + 9x + 36
Find the set of possible rational zeros given the function. 4) f(x) = 2x3 + 9x2...
Find the set of possible rational zeros given the function. 4) f(x) = 2x3 + 9x2 + 12x - 8 Find all the zeroes given a factor. 5) f(x) = x3 - 5x2 + 4x + 6 and (x-3) is a factor. 6) f(x) = x3 - 8x2 + 18x - 12 and (x-2 is a factor.
Problem 3. Earlier this semester, we proved the Fundamental Theorem of Algebra using an application of...
Problem 3. Earlier this semester, we proved the Fundamental Theorem of Algebra using an application of Liouville's Theorem. This problem asks you to fill in the details of an alternate proof of the Fundamental Theorem of Algebra that uses Rouché's Theorem. Let p(2) = 20 + 01 + a222 + ... + an-12"-1+ anza be a nonconstant polynomial of degree n > 1. (a) First, we choose R large enough so that, if |:| = R, then ao +213 +222+...+an-12"-1...
For the polynomial below, 1 is a zero. f(x) = x^3 + x^2 + 8x -...
For the polynomial below, 1 is a zero. f(x) = x^3 + x^2 + 8x - 10 Express f(x) as a product of linear factors. f(x) =
Use the Rational Zero Theorem to find all real zeros. (Enter your answers as a comma-separated...
Use the Rational Zero Theorem to find all real zeros. (Enter your answers as a comma-separated list.) 9x^3 − 17x^2 + 25x + 3 = 0
4. -/1 points OSCAT1 5.5.321. Use the Rational Zero Theorem to find all real zeros. (Enter...
4. -/1 points OSCAT1 5.5.321. Use the Rational Zero Theorem to find all real zeros. (Enter your answers as a comma-separated list.) 3 + 6x2 - 9x - 54 - 0
296 POLYNOMIAL FUNCTIONS 34. f(x) 4x3 -62-8+15 33. f(x) = r + 3x + 4x 12...
296 POLYNOMIAL FUNCTIONS 34. f(x) 4x3 -62-8+15 33. f(x) = r + 3x + 4x 12 35. f(r) r +7x2+9a 2 36. f(x) = 9r +2x +1 37 f(x) 4x4 - 4313r2- 12 3 38. f(x)2x4 -7x3 14r2-15 +6 39 f(r) x4 + x+7x 9x 18 40. f(x) 6x4 +17r3 -55r2 + 16+12 41. f(z) =-3r4 - 83-122- 12 5 42. f(x) 8a4+50343r2+2x-4 43. f(x) = x4 +9x2 +20 44. f(x) x4 +5a2-24 1 45. f(x) - r7x3-7x2 12x 12...
Linear Algebra 1) For each of the following linear systems of equations I. 2x, x 3...
Linear Algebra
1) For each of the following linear systems of equations I. 2x, x 3 x,-4x2 = 4 3x, +2x-5 2x, + 3x2-6x3 x 3x2 + 2x 2 -x,-4x2 + 6x3 =-1 III. 5x1 + 7x2=-5 8x1-5x2 = 3 IV, 2 a. Identify corresponding linear algebra nomenclature (4x -b) b. Calculate the inverse of the coefficient matrix (4) for each system Calculate each by hand and check your results with an alternate hand calculation or alternatively through an suitable...
71
60. 321z+ 61.-2x3 + 5x2-3x+9=0 62. _x3 + 8x-12-0 Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in finding all real and imaginary root 0 to each equation. 一63. x3-4x2-7x+10=0 一64. x3 + 9x2 + 26x + 24 = 0 -65. r3-10x-3=0 66. 2x3-7x2 160 一68. x4-4x3 + 7x2-16x + 12 = 0 69, 6' + 25x2-24x + 5 = 0 70·6x3-11x2-46x-24 0 --71. x4 + 2x3-3x2-4x+4-0 72, x5 + 3x3...
9x2+22x+9 x3+5x2+7x+3 a. Factor the numerator and denominator using the rational zero theorem as needed). Include any factors with irrational zeros but leave quadratic irreducibles as they are (no real zeros) b. State all zeros of f(x) (excluding any complex). c. Determine all asympotes (lines) and any holes (points) if they exist.. d. Write all intercepts as points. Plot all the points and asympotes so far by drawing your own appropriate scale using a ruler. e. Use extra points as...
1. (10 pts.) For the following polynomial; a. Use the Rational Zero Test to list all possible rational roots b. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots C. Factor the polynomial completely. x3 + 4x2 + 9x + 36
Find the set of possible rational zeros given the function. 4) f(x) = 2x3 + 9x2 + 12x - 8 Find all the zeroes given a factor. 5) f(x) = x3 - 5x2 + 4x + 6 and (x-3) is a factor. 6) f(x) = x3 - 8x2 + 18x - 12 and (x-2 is a factor.
Problem 3. Earlier this semester, we proved the Fundamental Theorem of Algebra using an application of Liouville's Theorem. This problem asks you to fill in the details of an alternate proof of the Fundamental Theorem of Algebra that uses Rouché's Theorem. Let p(2) = 20 + 01 + a222 + ... + an-12"-1+ anza be a nonconstant polynomial of degree n > 1. (a) First, we choose R large enough so that, if |:| = R, then ao +213 +222+...+an-12"-1...
4. -/1 points OSCAT1 5.5.321. Use the Rational Zero Theorem to find all real zeros. (Enter your answers as a comma-separated list.) 3 + 6x2 - 9x - 54 - 0
296 POLYNOMIAL FUNCTIONS 34. f(x) 4x3 -62-8+15 33. f(x) = r + 3x + 4x 12 35. f(r) r +7x2+9a 2 36. f(x) = 9r +2x +1 37 f(x) 4x4 - 4313r2- 12 3 38. f(x)2x4 -7x3 14r2-15 +6 39 f(r) x4 + x+7x 9x 18 40. f(x) 6x4 +17r3 -55r2 + 16+12 41. f(z) =-3r4 - 83-122- 12 5 42. f(x) 8a4+50343r2+2x-4 43. f(x) = x4 +9x2 +20 44. f(x) x4 +5a2-24 1 45. f(x) - r7x3-7x2 12x 12...
Linear Algebra
1) For each of the following linear systems of equations I. 2x, x 3 x,-4x2 = 4 3x, +2x-5 2x, + 3x2-6x3 x 3x2 + 2x 2 -x,-4x2 + 6x3 =-1 III. 5x1 + 7x2=-5 8x1-5x2 = 3 IV, 2 a. Identify corresponding linear algebra nomenclature (4x -b) b. Calculate the inverse of the coefficient matrix (4) for each system Calculate each by hand and check your results with an alternate hand calculation or alternatively through an suitable...
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