How many and of which kind of roots does the equati f(x) = x3 + 2x2...
A polynomial P is given. P(x) = x3 - 2x2 + 4x - 8 (a) Factor Pinto linear and irreducible quadratic factors with real coefficients. P(x) = (x+2) (x²+4) (b) Factor P completely into linear factors with complex coefficients. P(x) = (x + 2)(x2+4) Need Help? Read It Watch It
9. Given f(x) = x4 + 4x3 + 2x2-8-8, a) How many zeros does f(x) have (including multiplicities)? b) List the possible rational zeros of f(x). c) Find all rational zeros of f(x). d) Find all the zeros of f(x).
* 5. Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 3; zeros: -2 and 2i (a) f(x) = x + 2x² + 4x +8 (c) f(x) = x2 – 2x² + 4x – 8 (b) f(x)= x + 2x2 - 4x + 8 (d) f(x) = x3 – 2x2 - 4x - 8
Characteristics of skeletal muscle cells Solve the equation in the real number system. 1) x3 +2x2-5x-6-0 B) I-2, 1, 3) C) 1-3,- 2) x3 + 6x2-14x + 16-0 B) (8) C) 1-8, 8 3) 2x3 -x2-14x +7-0 8) f(x) -4x3-19x2 + 19x + 6 A) x-intercepts:-2, 3, y-intercept: 6 B) x-in C) x-intercepts-,-1, 2; y-intercept: 6 D) x-in 9) f(x) = x3-4x2-x + 4 A) x-intercepts: 1. -1. 1, v-intercept: 1
5. Let p(x) = 6 - 27r+ 39x2 – 3x - 15 (a) (2 points) How many zeros (real and complex, possibly with repetition) does f(x) have? What theorem did you use to get this answer? (b) (3 points) Determine all possible rational roots of p(x). (c) (2 points) What values from part (b) are actually roots of p(x)? You do not need to justify your answer. (d) (6 points) Find all other real and complex roots of p(x). Show...
Problem 2: Compare performance of Newton's method and Muller's method on the problem of finding roots of a polynomial with real co- efficients by the method of deflation ·Write a code implementing deflation method for finding all roots of a polynomial using (a) Newton's method, (b) Muller's method . On the example of P(x)+2+4r+3, show that Newton's method can not produce complex roots when starts from real On the example of P(x) = x3+4x2 +4x+3, show that Muller's ·Show that...
9. Find the relative and absolute max and min of the following functions a. f(x)=x'+x b, f(x) = Vx+4 64 c. f(x) = x3-2x2 + 5 d. f(x)- x2+4 9. Find the relative and absolute max and min of the following functions a. f(x)=x'+x b, f(x) = Vx+4 64 c. f(x) = x3-2x2 + 5 d. f(x)- x2+4
1) Using Matlab, find all real and complex roots of the following polynomial equation: (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)=8 2) Using Matlab, find the root for the following system of equations. Both x and y are positive. a: (x^2)cos(y)=1 b: e^(-4x)+1
Determine the point at which the graph of 2x2 + 4x + 2 F(x) = x2 + 4x + 7 intersects its horizontal asymptote. (x, y) = (
Exercise 5. Extreme values (8 pts+12 pts) Let f(x, y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 2) The point (1,2) is: a. a local maximum for f b. a local minimum forf c. a saddle point for f