Construct the divided differences table that led to the Hermite polynomial p(x) = 2 – (z – 1) + (z – 1)² +(z – 1)°(z – 3).

Q: For n = 4 , Legendre polynomial is 94 (x) = (35x – 30a? + 3)/8 %3D Find all its four roots.

A:

Q: Two polynomials are defined in MATLAB as >>p=[5 03 2 0]; q= 0 -1]; lo find the zeros of T(s) =…

A: Matlab is a programming and numerical platform to compute values, analyze , create model.

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: Let P(x) be the Lagrange interpolating polynomial that fits the data(-1,2); (4,2) and (7,5). Then…

A:

Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

Q: Divide the polynomials by using an appropriate method. (8x" – 16k10 + 24k° – 32k*) + (84®) = O olo

A:

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

A:

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

A:

Q: Compute the first 5 Legendre Polynomials, Po(x), P₁(x), -P₁(x). (These These are > Solutions, P,…

A: What is Legendre Polynomial: Legendre polynomial is a collection of orthogonal polynomials of degree…

Q: Write a polynomial ƒ(z) of degree 3 given zeros 4and 5i

A: Given a polynomial f(x) of degree 3 and zeros : 4 and 5i We know, complex zeros occurs in conjugate…

Q: Open with 1.9.1 Dividing Polynomials conmuer (Conthua Using the previous example, complete the…

A:

Q: Determine the standard form of the following polynomial: p(x) = (2x²+1)(x²-3)

A:

Q: find all polynomials P(x) and Q(x) satisfying, for all x∈R the equalities: P(Q(x))=x4-5x2+7 and…

A:

Q: Let f(x) = 4x4+x3+2x+1 and g(x) = 3x2+2x+3 be two polynomials in Z5[x].  Determine the quotient and…

A: We have to solve given problem:

Q: Express the polynomial in the form an(x - ₁)(x-₂)(x-rn). x² + 11

A: The polynomial is given by x2+11 To determine: The expression of the polynomial in factored form.

Q: 4. Express the greatest common divisor of the following pairs of polynomials as a combination of the…

A:

Q: Which of these polynomials has a zero of multiplicity 3 at z = 1? a. p(r) = xª + 5x³ + 5x² – 5x – 6…

A: If x=a is a zero with multiplicity n of a polynomial, then x-an is a factor of the polynomial. a.…

Q: Give the degree and leading coefficient of the following polynomial function. f (x) = x³ (3 – 7x² –…

A: Here in the given polynomial, we have to find the degree and order of the polynomial.   The highest…

Q: Determine the Newton's Divided-Difference Interpolating Polynomial P,(x) written in Newton's…

A:

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x,…

A:

Q: Find a polynomial p such that p(−1) = 0, p(4) = 0, and p(2) = 3

A: For a polynomial p(x),p(-1) = 0p(4) = 0p(2) = 3

Q: Use the given polynomial function to answer the questions. f (x) = x² (2x – 1)² - What is the degree…

A:

Q: Given (xi, x2024) Vi = 0,...,n, where x0 = -1, x₁ = 0, x2 = 1, x3 = 2, ..., xn = n = 1. Write down…

A: (a). When n=1, we have to points: (x0​,x02024​)=(−1,1) and (x1​,x12024​)=(0,0).  The interpolating…