3. Write down the polynomial having coordinates in B and the one with the same coordinates in B'.

Q: 2. Use syntr dhe hirst polynomial by the second. а. х2+x -3; х-1 b. 4x- 3x2+ 3x - 2; x-1 c. x'+x°…

A:

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

A:

Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: Is 7x to the 3rd power a polynomials

A: A polynomial is an algebric expression with at least one term in it.Given expression is 7x3. Here…

Q: Express the polynomial a+ 3 +a2 + 2r as a product of its irreducible factors in Z,lr).

A:

Q: (c) x + 4x + 2x + 3x -x+5 (4) x + Sx + 4x + 7 19. Write euch polynomial as a product of irreducible…

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

A:

Q: Find the linear polynomial p(x) = a1x + ao, that interpolates the two points with coordinates (3, 0)…

A: Given query is to find the equation of the line.

Q: Determine whether the first polynomial can be expressed as a linear combination of other two…

A: The given polynomials are  2x^3 − 2x^2 + 12x − 6, x^3 − 2x^2 − 5x − 3, 3x^3 − 5x^2 −4x − 9

Q: 16. Find a fourth degree polynomial that has the zeros 3, -2, i.

A: Given data: The first root of the polynomial is x1=3. The second root of the polynomial is x2=-2.…

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

A:

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

A:

Q: Fit a second-order polynomial to the data in the kollowing daha- 0|12/31415 yi 2.17.713.6|272 40.9…

A: The objective is to find a second order polynomial and to find the standard error.

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

A:

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: Ex.5 - Prove that the polynomial 2ª + z + 1 has exactly two zeros in the right half-plane.

A: Solution: We will be using the method of Routh array For a polynomial Qz=anzn+an-1zn-1+...+a1s+a0…

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

A: From the given data

Q: Find the polynomial in x of the third degree, which vanishes when x=-1 and x=2 has  the value 8 when…

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Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: If a polynomial cannot be written as the product of two other polynomials (excluding 1 and - 1),…

A: We know that a prime number have only 1 and that number as its factors.

Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

A: Newton's divided differences interpolation

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

A:

Q: A third degree polynomial passes through the points (0,-3),(1,0) (2,9), (3,30), (4,69) and (5,132),…

A: See the attachment

Q: Express the polynomial x3+2x+3 in Z5[x] as a product of irreducible polynomials of Z5[x] .

A: Explanation of the answer is as follows

Q: 1. Determine whether the set S = {2x² – 14x + 34, 3x – 4, x² + 5x + 1} is linearly independent or…

A: Here first we check the set s is linearly dependent or not.

Q: Form the polynomial function that has the following real ZEROS: 3,-1, 2, 4 Section 3.1 O z4 + 2z3 -…

A: Given point is; x = -3,-1,2,4   1) x4+2x3-14x2-13x+24  we find the factor of this function and then…

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: Express p(x)= x3 as a Taylor polynomial about a = -1.

A: The Taylor polynomial of degree n about  is given by:f(x) = f(a) + f'(a)(x-a) + f''(a)2!(x-a)2…

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: 8. Construct a polynomial with Z coefficents with a root of the given C 3+ V5 (a) (b) 2+ 3і (c) 1-…

A: We have to solve the given problem.

Q: 3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 y 1 -1 3…

A: From the given information, x0=0,x1=2,x2=4,x3=6 and y0=1,y1=-1,y2=3,y3=4. Formula for Lagrange's…

Q: If a, Band y are the zeroes of the polynomial p (x) = ax'+ 3bx² + 3cx+ d and having relation 2B =…

A: Option (c) is correct.

Q: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True…

A:

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

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Q: 1. Write the equation to the polynomial with double roots at 3 and 6, that levels off as it passes…

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Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

A:

Q: 4. Use synthetic division to find ALL the roots of f(z) of these. = z' + 26z³ + 10z² + 25z + 250 if…

A: Let w be a root of the polynomial f(z) then  f(z)=(z-w)g(z) Where g(z) is a polynomial of degree…

Q: Find the conditions that the zeroes of the polynomials Ax) =x – px+ qx – r may be in arthametic…

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Q: consider the function y=ax2+bx+c, where a is in the set {n∈ℕ|15}, b is an integer less than 10, and…

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Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Solution:- Any given value is said to be upper bound for the zeros of the polynomial if all the…

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

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

Q: Which of the following polynomials has zeros at x = -6 (which is a bounce point), and x = 4 (which…

A: Given data  Polynomial has zeros at x=-6(bounce point) Polynomial has zeros at x=4(cross point)…

Q: Find a forth degree polynomial that has the zeros 3, -2, i.

A: Explanation and Solution is given below....

Q: find the four zeroes of the polynomial z^4+4, one of them being z0=2^1/2e^ipi/4=1+i.then use those…

A:

Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…

Q: Find Ao, A1, and 4, in rewriting the function of ()- r>0 in terms of Lagure polynomial, /)=4L(*).

A:

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

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.