Given 2 distinct values x₁ and x₂(modp), we pick a polynomial P(x) of degree at most 3 at random. What's the probability that P(x₁)=P(x₂)(modp)
Given 2 distinct values x₁ and x₂(modp), we pick a polynomial P(x) of degree at most...
Suppose that P is a polynomial of degree n and that P has n distinct real roots. Prove that P(k) has n-k distinct real roots for 1≤ k ≤ n-1.
Question 1 2 pts The Hermite Interpolation polynomial for 33 distinct nodes has Degree at most {Be Careful with the answer. Look at the Theorem and the Question Carefully; compare the given information} Question 2 2 pts If f € C4 [a, b] and p1, P2, P3, and p4 are Distinct Points in [a, b], Then 1. There are two 3rd divided differences 2. There is exactly one 3rd divided difference and it is equal to the value of f(iv)...
with distinct nodes, prove there is at most one polynomial of degree ≤ 2n + 1 that interpolates the data. Remember the Fundamental Theorem of Algebra says a nonzero polynomial has number of roots ≤ its degree. Also, Generalized Rolle’s Theorem says if r0 ≤ r1 ≤ . . . ≤ rm are roots of g ∈ C m[r0, rm], then there exists ξ ∈ (r0, rm) such that g (m) (ξ) = 0. 1. (25 pts) Given the table...
Let f (x) be a monic polynomial of degree n with distinct zeros ai,..., an. Prove -1 Let f (x) be a monic polynomial of degree n with distinct zeros ai,..., an. Prove -1
Find a polynomial p(x) of degree 2 that satisfies , , and where a, b, c are given constants and are two different points. Thank you! We were unable to transcribe this imagep(m) = a We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
The polynomial of degree 4 The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = – 2. It goes through the point (5, 7). Find a formula for P(x). P(x) =
Please answer problem 4, thank you. 2. The polynomial p of degree n that interpolates a given function f at n+1 prescribed nodes is uniquely defined. Hence, there is a mapping f -> p. Denote this mapping by L and show that rl Show that L is linear; that is, 3. Prove that the algorithm for computing the coefficients ci in the Newton form of the interpolating polynomial involves n long operations (multiplications and divisions 4. Refer to Problem 2,...
Write a polynomial, P(x), in factored form given the following requirements • Degree: 3 • Zeros at (8,0), (2.0), and (-5.0) • intercept at (0,80), Provide your answer below: P(x) = 0
Given the graph of a degree 4 polynomial below, complete the table of values for either the x-value of a zero, or the multiplicity of the zero. Root with x - Multiplicity 4 2 4 3 2 1 2 3 5 -N -4 - 5 Submit Question
please help Write a polynomial of degree 3 that has three distinct x-intercepts and whose graph rises to the left and falls to the right. Choose the correct answer below. OA. f(x)= (x-7Xx + 3) fox)=(x +7)2(x-3)x+2x-1) C. f(x)=-x(x+7)(x + 3) O D. f(x)=-(x-3x-2) O B