Find all n EN for which is the polynomial x2n + x" +1 divisible by (x)f g(x) = x² + x + 1?

Q: Find k such that f(x) = x3 - kx2 + kx + 2 has the factor x - 2.

A: The general polynomial equation of degree n  is an equation of the form…

Q: 29. Write a third-degree polynomial f(x) with integer coefficients and zeros of i, -3, and 3.

A: Given  zeros of a third degree polynomial 14,−12 and 3

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: Let p > 2 be a prime number. If f(x) = 1' + x* + x² - x +1 € Z,[F] is divisible by the polynomial z…

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Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: Form a polynomial f(x) with real coefficients having the given degree and zero  Degree 4; -5+3i; -1…

A: It is known that if a+bi is a zero of polynomial with real coefficients then a-bi also a zero. Given…

Q: Find a polynomial with integer coefficients that has degree 4 and zeros 1−2i and 1, with 1 a zero of…

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Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inversein Z4[x].

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

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Q: 5. Find a polynomial of degree 4 with the zeros 3i and-v6j

A: Explanation of the solution is given below...

Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

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

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Q: Determine the third and fourth Taylor polynomials of x^3 + 3x - 1 at x = -1.

A: To determine the third and fourth Taylor polynomials of  x3+3x-1 at x=-1

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

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Q: ld and p (x) be an irreducible polynomial of positive degree over a

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Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3, and…

A: Let Q (x) be a polynomial that has degree 3, and zeros 0 and i. We know that if a+ib is zero of a…

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

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Q: Let f(x) = x, the second Taylor polynomial P2(X) about Xo = 2 is: Select one: O 1+ 3x + 6x? 08-12x +…

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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: 6- Show that the Polynomial has a Z4 [x] 2X+1 in multiplicative invers. in 24 [x].

A: Given

Q: A polynomial of degree n  1 has exactly zeros ifa zero of multiplicity m is counted m times

A: A polynomial of degree n≥1 has exactly  ___________  zeros if a zero of multiplicity m is counted m…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. F has degree 4 and…

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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: Prove that x2 + 3x + 3 > 0 for all x.

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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: .5) a) Express the polynomial f(x) in terms of Legendre polynomials where f(x) = 1-3x + 3x2

A: Given ,            f(x) = 1-3x+3x²

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

A: The given problem is to find the approximate roots using Newton's method in the given intervals…

Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

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

A: The given problem is to find the two real roots of the fourth degree polynomial at accuracy 10-6, we…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Given, polynomial R has degree 4, and zeros 1-2i and 1, with 1 being a zero of a multiplicity of…

Q: Show that f (x) = x2 + 3x−1 and g(x) = 3x3 − 9x + x−2 are rational functions—that is, quotients of…

A: To show: That the functions are rational function: Given: The functions are fx=x2+3x-1 and…

Q: Prove that x2 + 3x + 3 ≥ 0 for all x.

A: We have been given the quadratic equation  x2+3x+3

Q: Find a polynomial P(x) of degree 3 that has integer coefficients and zeros 1/2 and 3 - i.

A: 3-i+32+1=-i2+1=-1+1=0 So 3-i  is a zero of " x+32+1 ". . . . . . (1). 2·12-1=1-1=0 So 12 is a zero…

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

A: Find a polynomial of degree n=2 that has the given zero(s) x = −√2, √2

Q: 4. Consider the polynomial f(x) = x² + 1. (a) Show that f(x) is irreducible in (Z/3Z) [x]. (b) Show…

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Q: Find the integer a in Z5 so that (x-a) become a divider for f(x)=x^3+2x^2+3x+3 over Z5[x]

A: We have to find an a∈Z5 such that x-a is a divider for the polynomial fx=x3+2x2+3x+3 over Z5x. If…

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

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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: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 5; zeros:…

A: We know that whenever a complex number is a zero of a polynomial with real coefficients, its complex…

Q: The minimum polynomial of 5'3 over Q is x 1/3

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Q: find n∈ℕ is the polynomial f(x)=x2n +xn+1 divisible by g(x)=x2 +x+1?​

A: Given:            f(x)=x2n+xn+1             gx=x2+x+1

Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: Verify the assertion made in Example 2.

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

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

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Q: Find the value ofn EN such that the polynomial f(x) = (x+1)"+ (x- 1)" is divisible by g(x) = x.

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Q: Find a polynomial f(x) of degree 4 that has the following zeros. 8, 0, 5, -3

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Q: Show that, if gcd(a,n)=gcd(a-1,n)=1 then a is a solution of the polynomial parity x² + ... + xó(n)-1…

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