For the following exercises, use the given information about the polynomial graph to write the equation.Degree 4. Roots of multiplicity 2 at x = 1/2 and roots of multiplicity 1 at x = 6 and x = −2. y-intercept at (0,18).
The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a,
which happens to be positive. This real number a satisfies the
following properties:
- for i = 1,2,3,4,5,6,7,8,9,10, one has {a^i} not equal to
zero
- one has
[a] = 1, [a^2] = 3, [a^3] = 6, [a^4] = 11, [a^5] = 21, [a^6] =
7, [a^7] = 71, [a^8] = 130
(for a real number x, [x] denotes the floor of x and {x}...
The following cubic polynomial has three real roots p(x) =
32x3 − 110x2 + 123x − 45
(a) Plot p(x) for .9 ≤ x ≤ 1.6 and indicate the locations of the
three roots. What are the exact roots of p(x)?
(b) Write a MATLAB code to run Newton’s method with
x0 = 1.2 and discuss the convergence.
(c) Write a MATLAB code to run the secant method starting with
x0 = 1.31 and x1 = 1.2 and discuss the...
Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x=−2. y-intercept at (0, 4). For the above exercises, use the given information about the polynomial graph to write the equation.