Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2 = 2,x3 = 3,x4 = 4 , and x5 = 5 can be written as P(х) %3 Со + с, (х —- 1) + с, (х — 1)(х - 2) + с, (х — 1)(х - 2)(х — 3) +C,(х — 1)(х — 2)(х — 3)(х — 4). What is the value of c,? (A 0.00497 B -0.418002 © 0.06801 1.06783

Q: Find a polynomial f (x) of degree 5 that -4, -1, 3 (multiplicity 2), 0 Leave your answer in factored…

A:

Q: Find a fourth-degree polynomial with integer coefficients that has zeros 2i and -1, with -1 a zero…

A:

Q: Find a polynomial function with real coefficients that has the given zeros.2, 2, 1 + i

A: Given- The roots are 2,2 and 1+i. To Find- The polynomial function.

Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

A:

Q: 35. Write a third-degree polynomial f(x) with integer coefficients and with zeros of -2i and.

A: Given: A third degree polynomial with integer coefficients and with zeros of -2i and 5/3. Concept…

Q: Find the Maclaunin polynomial of degree 3 for the fuction. - ge

A: The given function is:fx=e-9xTo find the Maclaurin polynomial.

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

A:

Q: Give an expression for f(x) with leading coefficient –5, of degree 3, and having roots ¤ : -4 , x =…

A: from the given data: i^2= -1 Substituting in the required place and finding the polynomial

Q: Express the polynomial x3 + 2x+3 EZ-[x]as a product of irreducible polynomials of 75[x].

A:

Q: 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of…

A: Solution is given below:

Q: Factor f(x)=2x^3+5x^2-83x+40 into linear fuctors given that -8 is a zero of f(x)…

A:

Q: Degree: 4 ; Roots: x=0, x=i

A:

Q: Find a polynomial function with real coefficients that has the given zeros: 1,1, 2+√3i.

A:

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

A: The objective is to find the value of 2c3-c2

Q: 1. Using the points xo = 1 , x1 = 1.6, and x2 = 2.5, find the Lagrange interpolating polynomial that…

A: We find the Lagrange interpreting polynomial using the given points and that fits the function 2/x2.

Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

A:

Q: Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): 3,3,-1 .…

A: see 2nd step.

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula f(X;) Af(X,) A²f(X,)…

A:

Q: find the polynomial of degree 3 with zeros that include 3i, 3 and P(1)=3

A: The given zeros of a polynomial function are 3i and 3.

Q: 7. The fourth-degree polynomial f(x) = 230x* + 18x + 9x? – 221x -9 has two real zeros, one in [-1,0]…

A: As per the guideline, I am doing the 1st method only. Kindly repost the others separately.   Secant…

Q: Q-3: Plot the zeros of each polynomial on a line together with zeros of its first derivative. 1. y =…

A:

Q: If f(x)=ln(x) and x,-3.1, x₁-3.2, x-3.16, then the error bound in Lagrange interpolating polynomial…

A: Given the function is fx=lnx and x0=3.1, x1=3.2, x=3.16

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

A:

Q: 3. f(x) = x2- 4x- 5 4. f(x) = X2 - 9x - 36 (x-12)(x+3) roots are x=12 x=-3 5. f(x) = x2+ 3x- 40 6.…

A: Given3)f(x)=x2-4x-55)f(x)=x2+3x-406)f(x)=x2+22x+21 To find Roots of above

Q: Find a polynomial f (x) of degree 5 that has the following zeros. 3, -4 (multiplicity 2), 7, -2…

A: Find a polynomial F(x) of degree 5that has the following Zeros3,-4 (multiplicity 2) , 7,-2

Q: Factor f(x) = 2x + 9x- 33x + 14 into linear factors given that -7 is a zero of f(x). f(x) = 2x°…

A:

Q: 6. True or False A polynomial function of degree 4 with real coefficients could have -3, 2 + i,2 -…

A: True or False A polynomial function of degree 4 with real coefficients could have -3, 2+i,2 - i, and…

Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

A:

Q: what is the approximate value at point x- 0.7 of the interpolation polynomial obtained using the…

A: We have the following values: x y -1 4 0 11 1 16 2 13 Now, let make the backward…

Q: 3. Solve for all the roots of x using Bairstow's Method starting at ri = 0.25 and s1 = 8.75 of the…

A: We will use the basic knowledge of Bairstow's method to precisely find all the real and complex…

Q: For a function  f , the Newton divided-difference formula gives the interpolating polynomial P3(x)…

A: Given data: The given interpolating polynomial is P3(x)=1+4x+4x(x-0.25)+(16/3)x(x-0.25)(x-0.5). On…

Q: t is known that the polynomial p(x) = 2- (r+ 1) + x(x+ 1) – 2x(r + 1)(r – 1) interpolates the first…

A: Given:- p(x)=2-(x+1)+x(x+1)-2x(x+1)(x-)  interpolates the first four points of the table. x -1 0…

Q: The Taylor polynomial of degree 100 for the function ƒ about x = 3 is given by (x – 3)100 50! 2n…

A:

Q: Given that the interpolation error is E, (x – x1)(x – x2) ...· (x – xn). (n+1)! Why is the error…

A: We have the interpolation error is En=fn+1ξ(n+1)!x-x1x-x2...x-xn Now, the roots of the Chebyshev…

Q: (4) Find a polynomial that has 1+i and 1- i as zeros.

A: We have to find polynomial

Q: Using Newton's Divided Difference, the polynomial that interpolates ex at the points Xo=0, x1 = 1,…

A:

Q: 6. Does there exist a polynomial of degree 4 with integer coefficients that has zeroes i, 2i, 3i and…

A: Complex root must be in conjugate pair

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: If the leading coefficient of an odd-degree polynomial function is positive, then the function…

A:

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

A:

Q: Mr. Bean has a 5th degree polynomial using only the variable x. Mr. Kelly has a different 5th degree…

A: Mr. Bean has a 5th-degree polynomial using only the variable x. Mr. Kelly has a different 5th-degree…

Q: Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): 2, 1, 5.…

A:

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange…

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree…

Q: find a polynomial function with real coefficients that has the given zeros 0, 3, 2i 4, 1+√3 i

A:

Q: Find the polynomial f(x) of lowest degree with only real coefficients and having the zeros 3+ V2, 3-…

A:

Q: Find a degree 3 polynomial having zeros -1, 2 and 5 and the coefficient of x^3 equal 1. The…

A: Here we find the polynomial whose zeros are given.

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

A:

Q: Find an equation with real coefficients for the polynomial that passes through the point (0,…

A: we have to find an equation with real coefficients for the polynomial that passes through the point…

Q: The 2nd degree polynomial that interpolates to f(x) = cosx + sinx at x = 0, x= π/2 and x = π is best…

A:

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.