Q.11: Factor out, relative to the integers, all factors common to all terms 1) 3x +6x' +9x 2) 8u'v - 6u'v + 4uv 3) 2x (u-3v)+5 y (u-3v)

Q: 2. Use the inclusion-exclusion principle to find the number of solutions to the equation r+y+: = 19,…

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Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

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Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: Example Solve z"+ 512U3+ j512=0 or Find all the roots of fl3)=2"+572V3+j5]2. 10 on What ure the ten…

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Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that…

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Q: 1. Find the 5roots of z1 = -V3+iv3. %3D

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

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: 8. Express as a polynomilal. Arrange your answer from term with highest degree to lowers degree *…

A: SINCE YOU HAVE ASK MULTIPLE  QUESTION IN SINGLE REQUEST. SO WE WILL BE ANSWERING ONLY FIRST…

Q: Find all roots of z(z² + 5x – 25) = 125 and their multiplicity: I = -5 with multiplicity 3 I = -125,…

A: Here we find all roots of    x (x2+5x-25) =125and their multiplicity

Q: 2. Count the number of rearrangements of the word TASTE in which no letter appears in any of its…

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Q: Prove that 1. 1. 1 + 1x 2'2x 3 1 = 1 – (п — 1) хп + 3 x 4

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Q: Show that [o 2] A 3 0 has no A = L-U factorization where L is lower triangular and U is upper…

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Q: 8 (2-15)*- 3-V5 (a) Express in the form p + q5, where p and q are integers. (b) Given that = ab°,…

A: To solve the given problem we use the following result (a - b)2 = a2 + 2ab + b2 , (a+b)(a-b) = a2 -…

Q: (7) 13. Find two positive numbers, z and y, such that their product is 500, and z +3y is as small as…

A: Topic: calculus

Q: with Zeros of 2i with integer coeRficients that haf E Puno

A: We need to find the polynomial of degree three with integer coefficient

Q: Show that ZV-6 is not a UFD by factoring 10 in two ways. Why does this prove that Z[V-6] is not a…

A: Given, Z-6 is not a unique factor domain.To find:Z-6 is not a principal ideal domain.

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

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Q: 1. Given that r + px+q and 4x +q have a factor (x-r) where p,q and r are non-zero. Show that 4p…

A: topic - quadratic equations

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: now that 6z2 - 77y = 123456789 has no integer solutions for z and y.

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

A: Answer

Q: 10. Prove that Z has no smallest element.

A: we will prove it by contradiction, Suppose x belongs to Z  is the smallest element.

Q: By using Naïve Gauss Elimination. 2х + у — z %3D6 х — 2у + z %3 -3 Зх + 2у — 2z %3D 12

A: Write the given system of equations as 2x+y-z=6x-2y+z=-33x+2y-2z=12 It can be written as…

Q: 6. Determine the number of roots, counting multiplicities, of the equation in the annulus 1 ≤|z|< 2.…

A: We use Rouche's Theorem for this problem

Q: Factor 19 into irreducible elements in the Gaussian integers, Z[i].

A: We have to factor 19 into irreducible elements in the Gaussian integers, ℤ[i]. Irreducible element :…

Q: By using Eisenstein's criterion we can conclude that the polynomials x^3+4x^2+3 and…

A: Using Eisenstein's criterion we can check a polynomial is reducible or irreducible. For that some…

Q: The Cholesky factorization of 53 is UTU where U is: 3 2 V5 5 -3 V5 1 3. 0 1/5] V5 5 3 0. 1

A: The given matrix is,5332

Q: To find P(0 ≤ Z ≤ 1.37) using Appendix C-1, find the row containing ----  in the far left column.…

A: Given information- We have given- P(0 ≤ Z ≤ 1.37) We have to use Appendix C-1. We have to find the…

Q: show that x'-15x +C= O has at most root on E2,2] one

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: -80 -(2)) lo mes 6 ai12+1 at novie (e 6) Determine the zeros and their multiplicities for f(x) =…

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Q: if n is a perfect square then n2 + 2n is not a perfect square. prove this

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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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: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…

Q: 5. Find the v alue of x. 5x – 4 x + 6

A: Given :    To determine : The value of x.

Q: Prove that the area of a square whose diagonal has length d is A = A = 1/2d². A square with a…

A: A square has diagonal length of d, we have to find its area.

Q: 8. Determine whether v(x) = r'+3|x| even, odd or neither. Discuss its symmetry.

A: Q8) Given: v(x)=x3+3x

Q: 8-JIE FCx²_ ye, y-z²) =• then Prove that + Xそ 2Z

A:

Q: 7. In quadrilateral FGHJ, FH and GJ bisect each other and FH = GJ. FG JH FJ GH What additional…

A: FH and GJ are bisector of each other.

Q: 7. Find a direct way of showing that the (2, 2)-entry of a 3 x 3 magic square with weight w must be…

A: Use the common form of 3×3 square matrix with weight w  to find (2,2) entry

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: Let x be a positive integer. Show that if x is a perfect square, then 7x* + 4x2 + x + 3 cannot be a…

A: Solution is given below. Please upvote