Does there exist a polynomial of degree 3 with real coeffi- cients that has zeros 1, -1, and i? Justify your answer.

Q: The fourth-degree polynomial f (x) = 230x* + 18x³ + 9x² – 221x - 9 has two real zeros, one in [-1,…

A: Bisection method: This method is also called the interval halving method and it is used to find the…

Q: 3. Express as a polynomial. Arrange your answer from term with highest degree to lowers degree *…

A: 3. (3x3+4x2-7x+1)+(9x3-4x2-6x) open all the brackets =3x3+4x2-7x+1+9x3-4x2-6x rewrite or arrange…

Q: What are the zeros of the polynomial p (x) = (a - 5) (3x + 5) (x2 – 7x + 12)? %3D Express them in…

A:

Q: Find a fourth degree polynomial with real coefficients that has zeros of -3, 2, i that passes…

A: Let us consider a fourth-degree polynomial:

Q: Find a polynomial of degree 4 with 9 as a zero of multiplicity 1 and 4 as a zero of multiplicity 3

A: A polynomial of degree n has a zero  a  of multiplicity k iff (x-a)k is a factor of polynomial

Q: Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros -1,…

A: Given: Find a polynomial of the specified degree that satisfies the given conditions.Degree 4; zeros…

Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

A:

Q: Compute the zeroes of the polynomial 4x2 - 4x -8 also establish a relationship between the zeroes…

A: Given Polynomial 4x2-4x-8 = 4x2-8x+4x-8  = 4x(x-2)+4(x-2) = (4x+4)(x-2) In order to find the zeros…

Q: A certain polynomial has a root with a multiplicity of 3. What does this tell you about the behavior…

A: Given: A certain polynomial has a root with a multiplicity of 3.

Q: 1) Sketch a cubic polynomial whose zeros are -1, 2, and 9

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Q: Determine whether the following statement is true or false. If false, explain why. A polynomial…

A:

Q: A 4th degree polynomial has zeros -5, 3, i, and -i. Which could represent the function defined by…

A: here it is given that A 4th degree polynomial has zeros -5,3, i and -i

Q: Give one example of a polynomial of degree 4 that has a zero at x=5 with multiplicity 2 (there is…

A:

Q: Find a polynomial of the specified degree that has the given zeros. Degree 3; zeros -1, 1, 3

A: Given, Degree = 3 Zeroes = -1, 1, 3

Q: find a polynomial of degree 4 with zeros -6,-1,0, and 3.

A:

Q: Form a polynomial with a Degree 4; zeros:4+2i, -1 multiplicity 2

A:

Q: find the polynomial of degree 3 with zeros that include 3i, 3 and P(1)=3

A: The given zeros of a polynomial function are 3i and 3.

Q: Show that a polynomial of degree 3 has at most threereal roots

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Explain why a polynomial with real coefficients of degree 3 must have at least one real zero.

A: Given, A 3rd degree polynomial with real coefficients. Since the given polynomial is of degree 3,…

Q: Select the factors that multiply to create a polynomial with this description: (1) As x→-0, y→-∞ (2)…

A: Given x→-∞ and y→-∞ and x→∞ and y→∞ and x=4 is a root

Q: Find a polynomial of the specified degree that has the gi Degree 4; zeros -2, 0, 2, 4

A:

Q: Write a polynomial f (x) that satisfies the given conditions. 1 1 (multiplicity 1) and with f(0) =…

A: f(x)=ax+15x+15x-12 f(0)=a·15·15·-12 1 = -a50 a = -50

Q: Give the degree of the polynomial. 7 9 -vy

A:

Q: What is the polynomial, in factored form, for the function with the leading coefficient 6, and zeros…

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Q: Sketch a higher degree polynomial with the following roots: -2, 3, -3, 6. f(x) 9,

A: It is given that the roots are -2, 3, -3 and 6. That is, x+2=0, x-3=0, x+3=0 and x-6=0. The…

Q: A rectangle has a length of 18 units and a width of 14 units. Squares of x by x units are cut out of…

A:

Q: 4. Is it possible for a 6th degree polynomial with real coefficients to have 6 imaginary solutions ?…

A: To explain about the polynomial

Q: Give one example of a polynomial of degree 4 that has a zero at x = 5 with multiplicity 2. (There is…

A: Given: The given degree for the polynomial is 4. the given zero of the polynomial is x=5.…

Q: find a degree 3 polynomial having zeros 7, -3, and -8 and leading coefficient equal to 1.

A:

Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: Polynomial of lowest degree with zeros of -2 (multiplicity 2) and 3 (multiplicity 2) and with f (0)…

A:

Q: show that the polynomial below has a root between 0 and 1.

A: Given f(x)=2x3-11x2+18x-6 to find the root of the polynomial which lies between 0 and 1

Q: does there exist a polynomial of degree 3 with real coefficients that has zeros 1, -1, and i?

A: Consider the given roots. 1,-1, i and -i for complex roots. Now, make the polynomial.…

Q: find a degree 3 polynomial with zeros -2,1, and 5 and going through the point (0,-3)

A: Assume a polynomial and use the given point.

Q: Suppose​ f(x) is a 7th degree polynomial. Using a few complete​ sentences, explain why we are…

A: Given f(x) is a 7th degree polynomial.  Recall: fundamental theorem of algebra:  If f(x) is a…

Q: Which type of polynomial satisfies f ,,, (x) = 0 for all x?

A: Let f(x) be a polynomial such that f'''(x)=0 for all x Integrating both sides ,we get Again…

Q: Give one example of a polynomial of degree 3 that has a zero -6 with multiplicity 2

A: Consider the polynomial of degree 3, fx=x3+11x2+24x-36 At x=-6,…

Q: Write a polynomial f (x) that meets the given conditions. 4) Polynomial of lowest degree with zeros…

A:

Q: Does there exist a polynomial of degree 4 with real coefficients that has zeros i, 2i, 3i and 4i?…

A: Given statement : Does there exist a polynomial of degree 4 with real coefficients that has zeros i,…

Q: Find a polynomial of the specified degree that satisfies the given conditions. Degree 4  zeros −1,…

A:

Q: Find a polynomial of degree 3 that has zeros 5, -5, and 8

A: Given :To determine the polynomial ofdegree 3 has zeros 5,-5 and 8.

Q: Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros -1, 1, 3, 5

A: The objective is to find a polynomial having Degree 4 and zeros -1, 1, 3, 5.   By factor theorem,…

Q: write the polynomial f(x) that meets the given conditions polynomial of lowest degree with zeros of…

A: From the given condition, it is observed that the zeros are -2, -2, 3, 3 and f(0) = -108.Note that,…

Q: Show that a cubic polynomial can have at most three real zeros.

A: Suppose that the polynomial

Q: Find a polynomial of the specified degree that has the given zeros. 0, -1, 5

A:

Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the…

A: Zeros of a polynomial: Let the other zero be kThen the equation of the polynomial…

Q: Give one example of a polynomial of degree that has a zero at x=5 with multiplicity 2

A: zero at x=5 with multiplicity 2

Q: Consider a quadratic polynomial with a negativ main coefficient and a negative discriminant. Which…

A: Consider a quadratic polynomial with a negative main coefficient and a negative discriminant. Which…

Q: Suppose that a polynomial function of degree 4 with rational coèfficients has -2 +51, 5-5 as zeros.…

A: Complex root :  The complex conjugate of a complex zero must also be a zero . So if you have any…