(i) Find the solutions z1, z2 of the auxiliary quadratic equation 22 + (5 + 10i)z² – 48 + 14i = 0. Here, and in the next part (i), any extraction of the roots of degree two of a complex u E C must be done with the use of a scientific calculator; to show your work, please make sure to provide (a) the code for a scientific calculator you have used and (b) approximations of the module r = |u| and the argument 0 = arg(u) of u to five decimal places. (ii) Find the roots w1, w2 of degree two of z1 and then the roots w3, w4 of degree two of z2, thereby obtaining all four solutions of the original equation.

(i) Find the solutions z1, z2 of the auxiliary quadratic equation 22 + (5 + 10i)z² – 48 + 14i = 0. Here, and in the next part (i), any extraction of the roots of degree two of a complex u E C must be done with the use of a scientific calculator; to show your work, please make sure to provide (a) the code for a scientific calculator you have used and (b) approximations of the module r = |u| and the argument 0 = arg(u) of u to five decimal places. (ii) Find the roots w1, w2 of degree two of z1 and then the roots w3, w4 of degree two of z2, thereby obtaining all four solutions of the original equation.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 7DE

See similar textbooks

Similar questions

If r1 = a + iβ and r2 = a - iβ are two complex roots to theauxiliary equation ar2 + br + c = 0 , then general solution ?
1.Solve the roots of the equation f(x)=-0.5x^2+2.5x+4.5 a.With the Graphical Method b.Using quadratic formula
Consider applying the Muller’s method to find the roots of the equation x^3 − x − 1 = 0.(a) How many real and complex roots are there for the equation? How do you tell? (b) Use the Muller’s method with initial guesses x0 = 0, x1 = 1, x2 = 2 to find the quadratic functionthat is needed to find the first estimate.
1) Use the quadratic formula to find the solution(s) to x2-3x=8. Express the larger root below in simplest exact form.
Find the value/s of k in the given equation in order to have two distinct imaginary roots: 2x2 + 4x - k = 0
2. Given that x4 −2x3 −7x2 +8x+12 = 0 has the roots −1 and 2, find the quadratic equation whose roots are the remaining two roots of the given equation, and find these roots.
Find the 3 roots of the equation x3-1.25x+0.25 using BAIRSTOWS METHOD. USE r=1 amd s=2
Given the quadratic equation 0.987x^2+11.2x+0.246=0. Find the best approximation to each of the two solutions using 3 digit chopping arithmetic and the appropriate equations for x1 and x2
For the quadratic equation 9x^2+(3k+1)x+4=0 find the value(s) of k so that there is 1 real root.
Find the roots of Z²- 4Z+13 = 0
Find the value of k from the given equation which have two equal roots 2x2+kx+3=0
1. Find the quotient of x3 −5x2 −2x+ 24 by x−4, and then divide the quotient by x−3. What are the roots of x3−5x2−2x + 24=0? 2. Given that x4 −2x3 −7x2 +8x+12 = 0 has the roots −1 and 2, find the quadratic equation whose roots are the remaining two roots of the given equation, and find these roots.