+ .... Ex. 5. Prove that P,(-) = P,(-}) P,(4) + P,(-1)P2m -1 () + -. Pa(-)P.().

Q: Consider Z[x] = {a,x" + a₁₁x¹+...a₁x+ao: a; € Z,i = 0,1,2,...,n), the set of all polynomials in…

A: Inverse elements are 1 and -1

Q: What are Bernstein polynomials?

A: A polynomial is basically a function, which can either be quadratic, cubic and so on in which the…

Q: Find a quadratic polynomial whose sum and product respectively of the zeroes are as given .Also find…

A:

Q: Find the roots of the following using the indicated method|f (x)|< 0.0001 2. ƒ (x) = e2# + e# – 1,…

A:

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: A 9.7 100.3 B 8.3 109.5 C X 93.5 D 11.7 125.7 E 8.0 117.5

A: The given points are A(9.7,100.3),B(8.3,109.5),D(11.7,125.7),E(8,117.5).   We have use Lagrange…

Q: PC=2х7-5x6+4x4-3*3+2*-4

A: We can use the intermediate value theorem and the fact that polynomials are continuous functions to…

Q: 2. Find 52019 (mod 13).

A: Here,given  52019(mod 13)Now we find 52019(mod 13) using Chinese Remainder Theorem and Fermat's…

Q: Define the upper bound for the error in a Chebyshev polynomial?

A: To Define: An upper bound for the Chebyshev polyomial.

Q: Show that 1 + i is a root of x* - x' + x2 + 2. Use this fact to decompose the polynomial into a…

A:

Q: Find a 6th-degree polynomial with a negative leading coefficient that has roots x= 1- (square root…

A:

Q: 1) f (x) = 10.09x² + x4 + 17.64 2) f(x) = x3 + 9 %3D

A: We will use Muller's method to find the root of each of these equations using Muller's method.

Q: Define the Newton form of the interpolating polynomial?

A:

Q: Zero of -3 having multiplicity 3 and f(3) = 36 x = -3√ x = 3₁ x= 3√√x=3 +3)(xx-3)(x-3)(x-3)(x-3)…

A:

Q: What is the polynomial of degree zero

A: Degree of Polynomial: In a polynomial highest power of variable is called degree of polynomial.

Q: OUp3 Fee/X = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.

Q: Which of the following taylor polynomials is an approximation of the solution to the following…

A: We need to solve D.E.

Q: Are u able to do polynomial fitting without any mathematical tool? Why?

A: Polynomial fitting manually: a: Polynomial coefficient k: degree of polynomial N: no. of points to…

Q: Must the values be ordered from smallest to largest for the method to findNewton polynomials to…

A:

Q: Bisection me taad to find root of fal= XeXa! use the

A:

Q: Prb $2 x sinx dx メt)

A: We have to Solve given Improper Integral using Residue Theorem as Follows :

Q: Factor x12 - 1 as a product of irreducible polynomials over Z.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: what is a polynomial of the degree 4 with the interger coefficients with zeros of 1+3i and 2 (with 2…

A: we are given zeros as