If p(x) is a polynomial in Zp[x] with no multiplezeros, show that p(x) divides xp^n-x for some n.

Q: An nth degree polynomial will have at most n+1 real roots. O True O False

A: No, that is not possible. The only reason that an n-degree polynomial has max n roots is that it can…

Q: What type of polynomial satisfies f"(x)=0 for all x?

A: Topic-polynomial

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

A: Since x=-4 is a zeros so, (x+4) is a factor of f(x) Since x=1 is a zero so, (x-1) is a factor of…

Q: y = exp( 2-x ) at x = [-1,2].

A: Given   y=e(2-x) , in the interval x=-1,2 So the value of y at x=-1,0,1,2 are…

Q: Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and…

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Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)

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Q: polynömial that passes through the three points (0, 1), (1, 2) and (2, 23). If the coefficient of x…

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Q: If f(x) is a polynomial with real coefficients and zeros of 5 (multiplicity 2), –1 (multiplicity 1),…

A: The number of zeroes are 4. But one zero has a multiplicity of 2 that is the zero is repeated.

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

A:

Q: Express the polynomial x3 + 2x+3 EZ-[x]as a product of irreducible polynomials of 75[x].

A:

Q: Find a polynomial f (x) with leading coefficient 1 and having the given degree and zeros.

A: To find a polynomial  f(x) with leading coefficient 1 and having the given degree and zeros.  degree…

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

A:

Q: Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 2i as zeros.…

A: We know that "If the polynomial has only real coefficients, then any complex roots must occur in…

Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

A:

Q: If f(x) is a 4th degree polynomial, and has 3 real numbers as roots, the other root is?

A:

Q: Find ALL irreducible polynomials of degree 2 or 3 in Zr].

A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…

Q: In Z4{x}, find two distinct polynomials that determine the same function for Z4 to Z4.

A: we have to find two polynomial Z4 {n} which determine the same function for Z4 to Z4. Let us…

Q: Let f(x) = x' + 2x + 4 and g(x) - 3x + 2 in Z,[x]. Then, upon dividing f(x) by glx), we get 7- The…

A: I am solving part7 & part8 as you mentioned.

Q: Find real zero of f(x) = x* – 2x³ – 4x² + 4x + 4 within TOL = 10-5 by following methods:

A: First, plot the curve for f(x). Use the graph to find a real zero as mentioned in the question.…

Q: 8 (x)= 1 centered at a =0 1+x

A:

Q: If f(x) is a polynomial with real coefficients and zeros of 4 (multiplicity 3), –2 (multiplicity 1),…

A: The multiplicity means that the zero of the polynomial is repeating. For example, let's take a…

Q: 6. Use the Remainder Theorem to evaluate f(x) = 10x* - x3 + 13x2 – 9x + 17 at x =-.

A: Since the student has mentioned to solve question number (6), so we are solving only question number…

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

A: Iteration formula for secant method is:  xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn)…

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

A: If x=a is a zero with multiplicity n We have (x-a)n

Q: Find a polynomial f (x) with leading coefficient 1 and having the given degree and zeros.

A: The polynomial having leading coefficient 1 and degree 4 is starts from x4. The roots or zeros…

Q: Let f be an nth-degree polynomial and let g be an mth-degree polynomial. what is the degree of f * g…

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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: 32. If p(x) is a polynomial in Z,[x] with no multiple zeros, show that p(x) divides xP" . x for some…

A: Let F be a field, and suppose p(x) ∈ F[x]. hp(x)i is the set of all multiples (by polynomials) of…

Q: Find the polynomial with thats has degree 3 and Zeros 2,-1 and 3

A: To find the polynomial with thats has degree 3 and Zeros 2, -1 and 3.

Q: The fourth-degree polynomial f (x) = 230x4 + 18x³ + 9x² – 221x 9. - - has two real zeros, one in…

A: The given polynomial is - f(x)=230x4+18x3+9x2-221x-9 It is also given that the given function has…

Q: Express p (x) = x3 as a Taylor polynomial about a = 1/2

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

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Q: The polynomial f (x) leaves the remainder x + 2 at the division with x ^ 2 + 2x-3 and leaves the…

A: Use the remainder theorem for the polynomials to determine the remainder when f(x) is divided by…

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: Write the polynomial f(x) that meets the given conditions. Degree 3 polynomial with interger…

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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: 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: 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…

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Q: A polynomial which goes through the point (1,4) and has zeros at x=0,x=3 and x=-2

A: Given:A polynomial pass through the point (1,4) and has zeroes at x=0, x=3 and x=-2.

Q: Express p(x) = 1 + 2x -5x2 as a Taylor polynomial about a= -2.

A: p(x)=1+2x-5x2 a=-2

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: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8

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

A: Any polynomial function, f(x) that has roots, , can be expressed as   Here, are the multiplicities…

Q: Use syntheti¿ division to firid fiz) in f(x) = -x+5x²-7x+1

A: We have to find function value

Q: Express the polynomial x3 + 2x+3 EZ[x]as a product of irreducible polynomials of 75[x]- Attach File…

A: Use the definition of irreducible polynomial and property of ring Z_5[x].

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…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.