Let f(x) = 2x⁴ - x³ + ax - 1
If 2 is a root of the polynomial f(x), then f(2) = 0
f(2) = 0
2(2)⁴ - (2)³ + a(2) - 1 = 0
2(16) - 8 + 2a - 1 = 0
32 - 9 + 2a = 0
23 + 2a = 0
2a = -23
a = (-23/2)
Hence the required value of a is (-23/2).
Find the value of a such that 2 is a root of the polynomial 2.4 –...
2. (30%) Given 2 as one root of the following polynomial, find the remaining roots (that is, find all remaining roots but it is not necessary to show your calculation procedure/step to get full marks) 3x3 + 7x2 - 22x -8=0
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) =
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=1 and a root of multiplicity 1 at x=−5. The y-intercept is y=−3; Find a formula for P(x).
The polynomial of degree 3, P(x), has a root of multiplicity 2 at5 and a root of multiplicity 1 at z3. The y- intercept is y37.5. Find a formula for P(z). P(x)- Preview Get help: Videc License Points possible: 1 Unlimited attempts. Submit Write an equation for the polynomial graphed below -2 -3 y(x)- Preview Get help: Video Points possible: 1 Unlimited attempts. Submit Search or type URL calculus Section 22 Spring 2019> Assessment Write an equation for the polynomial...
in matlab Using the polynomial entered and the starting guess , compute the root of the polynomial using the Newton-Raphson method. Repeat the method until the percent error between the most recent two iterations is less than the percent error entered by the user . Determine the percent error of the most recent two iterations using the formula. Output the final value of the root found with the Newton-Raphson method and the number of iterations the method took to converge...
3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial
3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial
State the degree of the following polynomial equation. Find all of the real and imaginary roots of the equation, stating multiplicity when it is greater than one. X6 10x5 25x4-0 The degree of the polynomial is Zero is a root of multiplicity is a root of multiplicity 2.
using matlab
3. [1:2] Find a root (value of x for which f(x)-0) of f(x) = a x^3 + bx^2 + c x + d using Newton's interation: xnew = x -f(x)/(x). Note that f'(x) is the first derivative off with respect to x. Then x=xnew. Start with x=0 and iterate until f(xnew) < 1.0-4. Use values (a,b,c,d]=[-0.02, 0.09, -1.1, 3.2). Plot the polynomial vs x in the range (-10 10). Mark the zero point.
(1 point) Taylor's Remainder Theorem: Consider the function 1 f(x) = The third degree Taylor polynomial of f(x) centered at a = 2 is given by 1 3 12 60 P3(x) = -(x-2) + -(x - 2)2 – -(x - 2) 23 22! 263! Given that f (4)(x) = how closely does this polynomial approximate f(x) when x = 2.4. That is, if R3(x) = f(x) – P3(x), how large can |R3 (2.4) be? |R3(2.4) 360 x (1 point) Taylor's...
Write a matlab program to find the multiplicity of the root x = -0.5 of the polynomial x^5 -4.5^4 + 4.55x^3 +2.675^2 - 3.3x - 1.4375.