Suppose P(x) is a polynomial satisfying• P( – 4) = - 32• P'( – 4) = 44• P'(– 4) = – 90• P(3) (– 4) = 366• P(4) = 0P'(4) = 796IfP(2) = a + b(z – 4) + c(z – 4)(2 + 4) + d(æ – 4)(æ + 4)² + e(æ – 4)(æ + 4)³ + f(æ – 4)°(æ + 4)³then1. What is the coefficient a ?2. What is the coefficient b ?3. What is the coefficient c?4. What is the coefficient d?5. What is the coefficient e ?6. What is the coefficient f ?Attach your work in the following answer box as a pdf file of your Maple sheet.

The polynomial function P(x) where polynomial is a function of x , input any value of x the value of…

Answered: Suppose P(z) is a polynomial satisfying…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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How can the following problem be solved?
5. Obtain a polynomial P(x) such that f(x) = P₁(x) given the table -1 -3 x₁ f(x₂) -2 -13 1 -1 2 -9 3 17
1. Is (x-1) a factor of ƒ(z) = zª + 2x²−z+2? O f(-1) = 6, so (x-1) is not a factor. O f(1) = 0, so (x-1) is a factor. O f(1) = 4, so (x-1) is not a factor. O f(-1) = 0, so (x-1) is a factor.
10. Given that p(x) and f(x) are polynomial functions such that p(x) = xf(x) + c, determine c if the graph of p(x) is shown %3D (9,r) (0, t), (р, 0) (s, 0) A. p В.t С.r D. s
Without using a calculator, decide which of the equations A-E best describes the polynomial in Figure 62. A y = (x+ 2)(z+1)(z – 2)(z – 3) By = z(r+ 2)(x + 1)(x – 2)(x – 3) Cy = -(z+ 2)(r + 1)(x – 2)(r – 3) Dy = (z +2)(r + 1)(x – 2)(x – 3) E y = -(x + 2)(r+1)(r – 2)(x – 3) st -5 -10+ Figure 62
9. A polynomial function p(x) has exactly four roots: -2i, 2i, -5, and 1. Which of the following could be p(x)? p(r) = (x + 5) (æ – 1) (æ² + 4) p (x) = (x – 5) (x +1) (z² + 4) p (a) = (x + 5) (x- 1) (z² – 4) p(z) = (x5) (r + 1) (x + 4)²
18. Find the equation of the polynomial,fG, with the following properties. * Degree is 5 Zero at x = 2 with multiplhcity 3. Zero at X= - 2 Zeco at x1 yintercept (0,16)
6. A polynomial, p(x)=3x^4+Bx^3+Cx^2+x-2, has real coefficients. a. Show that P(x) has at least one positive and one negative real zero. b. Given that one of the zeros of P(x) is -4/3, what can we say for certain about B(the x^3 coefficient) and C (the x^2 coefficient?
11. The polynomial function y = x³ +ax² +bx+5 has a local minimum at æ = 1 and an inflection point at æ = -2. The values of a and b, respectively, are? O-3 and -24 -3 and 0 6 and -15 6 and 9
2. (a) Find the function P(x) = a + b сos(лx) + с sin(x), which interpolates the data X 0.5 1 4 (b) Find the quadratic polynomial interpolating this data. 0 2 y

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