If -1-x-1)), which polynomial represents )? A+1 (?'+1){x² -1) C. -+1-1 В. D. ++s+!

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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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: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

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Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: Now just as with Example 2.16, prove that if f, g, and three polynomials in R(r], then (f+ g) + h =…

A: Introduction: In mathematics, functions are the most fundamental aspect of calculus. Functions are…

Q: & Give an example of a polynomial (x) € Z[] and a prime p such that f(x) is reducible in Qx] but…

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Q: Find a polynomial of degree n=3 that has the given zero(s) x = −2, 6

A: A polynomial is an expression comprised of variables, their coefficients, constant, and exponents,…

Q: Show that x19 + x8+ 1 has multiple zeros in some extension of Z3.

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Q: In Z3×U3, Find the order of (1, 2). Show your work.

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Q: The zero-product principle states that if AB = 0, then________.

A: Zero-product principal:

Q: Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one…

A: Basic properties of modular arithmetic and gcd will be used in solving this problem. The detailed…

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

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Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: find a formula for the polynomial P(x) with degree 3 leading coefficient 2 zeros at -5, -3, and 3

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Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: Find a polynomial of degree n=2 that has the given zero(s) x = −3

A: Let us find a polynomial with a degree of 2 and a zero x=-3 A factored polynomial with a zero -3 has…

Q: 1 is a zero of the polynomial P(x) = x³ – 3x* + 7x³ – 13x² + 12x – 4 of multiplicity (а) 3 - - (b) 5…

A: 1 is the zero of given polynomial.

Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: Find a formula for the polynomial P(x) with degree 3  leading coefficient 1 zeros at 8, -6, and 7…

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Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

Q: 1. Find an r> 0 such that all zeroes of 24 + 6z²+z+3 are contained in D,(0).

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Q: Is the polynomial x2 – 4 in the ideal generated by the polynomials x + 22 – 4x – 4, x – 22 – 4x + 4,…

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

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: The zero-product principle states that if AB 0, then

A: If AB = 0Then zero-product principle states that this is possible only if - A = 0andB = 0

Q: Q2: Show that whether (Z16,O.O) is field or not?

A: Properties of a field For all a,b, and c∈F, the following hold: a+(b+c)=(a+b)+cand a⋅(b⋅c)=(a⋅b)⋅c…

Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

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Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: Find p so that  x2 - 6x + p = 0  has one root (i.e. is a perfect square)

A: We will solve it by two methods Shortcut method to find p for the equation given is x2 + b x + c  is…

Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: Does there exist a polynomial of positive degree in ℤ6[x]Z6[x] that is a unit?

A: First, we understand how units in R[x] are identified. Let R[x] be an integral domain. An element…

Q: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Show that 1 is the only solution of x25 - 1 = 0 in Z37.

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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: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

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: Given two polynomials in from of x^3+x^2+x+c =0 x^3+x^2+x+c =0

A: Given: To find their intersection using matrices. Given two polynomials in from of…

Q: 8 Σ n=1 an, an = ýnt + 4n3 + 6n2 – 3/ P(n)

A: Given : infinite series      ∑n=1∞an ,   an=n4+4n3+6n24-Pn3 To find : third degree polynomial Px…

Q: 5. Show that for Chebyshev polynomials (Tn, Tm) = 0, n #m, π, EIN n=m= 0, n = m = 0.

A: We have to solve given problems;

Q: The general polynomial of degreen has the form = a,x" + a,-1x"- + .. + azx? + ajx + ao, where a, +…

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Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: 18. Given the polynomial irrational roots. f(x)=2x²-x²-5 . use linear interpolation to approximate…

A: Given: The polynomial is fx=2x3-x2-5. To find: The roots of the given polynomial.

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

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Q: (a) State the Eisenstein Criterion (without proof). [ (b) Prove that 30x³ 91 does not have roots in…

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Q: 1. Use substitution technique to show that ++x+2+x- v2 +C dr 1 In rV+r+2 +x+2+r+ V2

A: As per our guidelines we are supposed to answer only one question that is the first question. For…

Q: 24. Determine the number of zeroes of the polynomial z7 – 6z5 + 8 in the annulus 1 < |z| < 2.

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Q: 4. Prove that f(r) = 4x³ - 8² + 2x + 1 has three real zeros. %3D

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