Roots and polynomials
If z is an n-th term of 1, show taht 1+z+z^2+z^3+....+z^n-1=0. Solve the equation with n=5 and hence factorize 1+z+z^2+z^3+z^4 into linear factors with complex coefficient and then into quadratic factors with real coefficients.
If z is an n-th term of 1, show taht 1+z+z^2+z^3+....+z^n-1=0. Solve the equation with n=5 and hence factorize 1+z+z^2+z^3+z^4 into linear factors with complex coefficient and then into quadratic factors with real coefficients.
Describe the steps in and/or define how to accomplish the following types of proofs: a. That two sets are equal. b. That two sets are disjoint. c. A proof by contra-positive. d. A proof by contradiction. e. A proof by Mathematical Induction. (Question is repeated in attachment)
Question in attachment is as follows: Consider all lines in the plane. If a relationship between 2 lines is defined by the expression that their slopes are equal, prove that this relationship is an equivalence relationship. If we consider the set of all lines in the plane, how would you uniquely identify the equivalence clas
Write a in terms of b for: a=(9^x) + 5 b= 3-(3^x)
If the lines ax-y=6 and 4x+(a+4)y=-6 are parallel, what is a=?
|x-4| + |x| = 8 what is the sum of the possible value(s) of x?
((x^2 +ax +b)/(x^2 +11x +28)) ((x^2 +4x -21)/(x^2 -9))= (x+2)/(x+3) What is a+b=?
Simplify (sqrt2 - (1/sqrt2))/(sqrt2 + (1/sqrt2))=?
Find the following limits using L'Hopital's rule. See attachment below.
Reducing the Size of a candy Bar: A jumbo chocolate bar with a rectangular shape measures 12 centimeters in length, 7 centimeters in width, and 3 centimeters in thickness. Due to the escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides the new bar
Factor: 75+12x^2+60x
2^3 * 2^-4 (from Modern Engineering Mathematics 3rd Ed Ex 1.2.5.1(a))
How do I determine the cardinality of an infinitely large set (such as real numbers)? What is c and 2^c mean?