the legendre polynomial pn (x) has .a none of these .b n zeros of which only one is between – 1 and 1. .C 2n-1 real zeros between -1 and 1. .d real zeros between and 1.

Q: Let f(x) be a polynomial function whose coefficients areintegers. Suppose that r is a real zero of f…

A: Consider an example:  2x3=x+6x+12x-42x3=x3+14x2-2882x3-x3-14x2+288=0⇒x3-14x2+288=0

Q: the legendre polynomial Pn (x) has none of these a O 2n-1 real zeros between -1 and 1.bo n zeros of…

A: We have to find the roots of Legendre polynomial and thus choose the option accordingly.

Q: (a) Find the Maclaurin polynomial p2 for V1- x and express the error with Landau's big O notation.…

A: Find: Maclaurin polynomial for √(1-x) and express the error with Landau's big O notation.

Q: VII. Write a polynomial f(x) that meets the given conditions. 11.) Degree 3 polynomial with zeros…

A: We have to find the function of polynomial which meets the given conditions.

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 3 and…

A:

Q: A polynomial is known to have the following roots x₁ = 4.9+ -4.3 i x2 = 2.3 x3 = (4.6) ¹/2 Determine…

A: If the root is complex number of a real coefficients polynomial then it has complex conjugate root.…

Q: Let p be a prime and let q = p². Show that Z,[x] has a unit that is not a constant polynomial.

A: Given that, Let p be a prime and let q = p ^ 2 . Show that Zq[x] has a unit that is not a constant…

Q: Let 0 be a root of the polynomial x³ + 3x + 7. Prove that 0 is prime in Q(0).

A: We will use the basic knowledge of polynomials and rings to answer this question properly, in…

Q: find a polynomial with integer coefficients that satisfies the given conditions.  P has degree 3…

A:

Q: find the equtions f(x) of a polynomial having following zeros: x=-1 with multiplicity 3 x=2 with…

A: equation of polynomial:-

Q: 6. Use the fact that every odd degree polynomial with real coefficients has a real root to show that…

A: Show that the function f:ℝ→ℝ defined as fx=x5-2x2+x is onto for all x∈ℝ. Definition:  A function…

Q: There is an inaccuracy in the following table of a low degree polynomial p(x). x p(x) 0.0 0.000 0.1…

A: The relationship between the data points can be observed using a difference table. Make Newton's…

Q: The following polynomial 2 points below is: p (x) = a + 3x + 2 not irreducible polynomial over the…

A:

Q: Consider the polynomial x +x + 1 in Z2[x]. Which of the following statements is true? O This…

A: In this question , we have to use concept of Irreducible polynomials. Irreducible polynomials If a…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

A: Given:Q is a polynomial of degree3roots :-9,1+i

Q: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers…

A:

Q: (d) The cubic Legendre polynomial is P₂(x) = (5x¹-32). Prove that it is orthog- onal (over [-1,1])…

A: To Prove: The given Legendre polynomial P2(x)=125x3-3x is orthogonal to all polynomials of degree 2…

Q: Find the Maclaurin polynomial P, to f(x) = ncosnx.

A:

Q: If f(z) is a polynomial In z such that when it divides by z-i and z+i,the remainder when f(z) is…

A:

Q: For the following, find the funchen p defined ha polynomial of degree 3 with real coefficients that…

A:

Q: Show that P(x) = (2n + 1) P(x) + P_1(x) n-1 where P(x) is a Legendre polynomial of degree n.

A:

Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and…

A:

Q: Given a function f (x) that passes through the points (1, 2), (2,−1), and (3, 4), use the Lagrange…

A:

Q: White a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer…

A: Given zeros of a polynomial,

Q: Find a second-degree polynomial P such that  P(2) = 3, P'(2) = 7,  and  P''(2) = 6.   P(x) =

A:

Q: 2) If f(0) = 0, f'(0) = 1, f"(0) = 0, and f''(0) = 2, then which of the following is the third-…

A: We will be using Maclaurin Polynomial result

Q: or the following find the function P defined by polynomial of degree 3 with real coefficients that…

A:

Q: Prove that for any polynomial P of degree <n, | P' (x) | < n(1 || P || - x²)-1/2 || P ||, where max…

A: We will construct another function in terms of P(x) and prove the given statement.

Q: Find a second-degree polynomial P such that  P(1) = 1, P'(1) = 2,  and  P''(1) = 4.

A:

Q: Consider the polynomial p(x) = x³ + x + 1 over Z₂. Denote by a = x+. Then a³ + a + 1 is a root for…

A: Using the property of ideal and ring

Q: 3. • Use sequential continuity to show that any polynomial P(x) = x" + a,n-17"-1+...+ ao %3D is…

A:

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and…

A: Given that the zeros of polynomial are 1 + i and 1 - i. To find the polynomial of P(x) has degree.

Q: Find a polynomial with integer coefficients that satisfies the given conditions P has degree 3 and…

A: Use factor form for polynomial

Q: 4. If the polynomial function P has real coefficients and if a + bi is a zero of P, then is also a…

A: We know, complex roots occurs in conjugate pairs. So if,x+iy, is a root of given polynomial…

Q: Which of the following polynomials in Z3 [x] is irreducible? (a) p (x) = x ^ 3 + x + 1 (b) p (x) =…

A: Useful result: If f(x)∈F[x] be a polynomial over a field F of degree two or three. Then f(x) is…

Q: (d) The cubic Legendre polynomial is P2(r) =(5x – 3r). Prove that it is orthog- onal (over [-1, 1)…

A:

Q: Use the intermediate value theorem to show that the polynomial has a real zero between the given…

A: The given function is

Q: The taylor polynomial of order 3 generated by f(x) - at a-0 81 x3 1 P = 3. 9. 27 81 x3 x4 6. 27 81…

A: Taylor polynomial

Q: 12. R sed e A fourth-degree polynomial P(x) satisfies A4P(0) AP(x) = P(x + 1) - P(x). Compute…

A:

Q: Consider the following polynomial. H(x) = x³ + x² – 10x – 10 - Step 1 of 2: Use the Rational Zero…

A: Rational zero theorem :-  Let P = anXn +an-1Xn-1........+a0 =0 be a polynomial with an.......a0…

Q: For any non-negative integer m show that In [x2m] is a polynomial in n of -degree m with integer…

A:

Q: the legendre polynomial pn (x) has n real zeros between 0 and 1. n zeros of which only one is…

A: It has only two singular points namely x = 1, x = −1 all are regular. Therefore, Legendre 's…

Q: If the polynomial P(x) is the nth Taylor's polynomial for f(x) about the point ro then the upper…

A: Solution

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and…

A: Let P is a plynomial that has  degree 2 and zeros  2 + i and 2 − i Then

Q: Which of the following statements couldn't possibly be true about the polynomial function P? (a) P…

A: The number of local maxima or local minima cannot be greater then the degree of a polynomial.

Q: 5.0 F10 10 -10

A:

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and…

A:

Q: In the set of polynomials in the form: P(x) = ax + bx' + cx² + dx + e, x E R there is a subset M,…

A: Given the polynomial M=px=ax4+bx3+cx2+dx+e, x∈ℝ|x,p(x)=-2,4,-1,0,1,-2,3,6. (a) Consider a cubic…

Q: 1 The cubic Legendre polynomial is P2(x) = (5x³ – 3). Prove that it is orthog onal (over [-1, 1]))…

A:

Q: Let a E Z2 be a zero of the irreducible polynomial x3 + x +1 over Z2. Show that the elements of B =…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.