**History of Mathematics**

Homework Assignment 3

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

1. Examine the equation for real roots using Descartes Rule of signs, and also see if it has any rational roots

(a)

(b)

(c)

Note: it is helpful to for each of the polynomials above to denote by the f(x) the polynomial on the left side of the equation. Now, compute the expression for f(-x). If the original equation has a negative root, it will show up as a positive root for f(-x) = 0.

2. If 3 + 2i is the root of a quadratic (polynomial) equation with integer coefficients, find the quadratic equation.

3. Find a polynomial equation whose roots are:

(a) 2, 4, -5

(b) 3, 3, -1

(c) +i, -i, +i, -i and 12

4. Solve the following equations:

(a) 2x = 6

(b) 2x = 7

(c) 2x - 3(x - 4) = x + 11

(d)

(e)

(f)

(g)

(h)