math 126 re write by tonight

Quads and Primes1

Quadratic Equations and Prime Numbers

Survey of Mathematical Methods

Shadd Campbell

MAT 126

March 11, 2013

Quadratic Equations and Prime Numbers

The first project prescribed this week pertains to quadratic equations. Quadratic equations date back to 1800 BC and 1600 BC. The Babylonians left the earliest evidence of quadratic equations, and provided methods for solving them. This week we look at the Indian quadratic equations and the method for solving them. Quadratic equation is defined as “one or more of the terms is squared but raised to no higher power, having the general form , where a, b, and c are constants” (American Heritage Dictionary, 2003). The second project prescribed this week deals with prime numbers. A prime number is defined as “a positive integer not divisible without a remainder by any positive integer other than itself and one” (American Heritage Dictionary, 2003).

Project 1: Bluman, 2005, page 331 (Equations A and C)

Equation A

b.

c.

d. √ ( = √56 √( = √56

e.

f.

The solution would be and

Equation C

0

a.

b.

c.

d. √ ( = √400

√( = √400

e.

= 4

f. x)

= -16

The solution would be and

Project 2: Bluman, 2005, page 331

First, let’s choose x = 0

(This is prime)

If we then substitute x = 2

(This is prime)

Then substitute x = 5

(This is prime)

Then substitute x= 7

(This is prime)

Finally, let’s choose x = 41

(This is a composite)

When we substitute 41 for x we get a composite number.

After completing this exercise I considered when an individual would us a quadratic equation. I found it very interesting that quadratic equations are used quite frequently by the military to determine missile trajectories. They use computers almost exclusively, but the computer bases the trajectories on the quadratic formula. The second use I found was for amplifiers in car stereos. Electrical engineers use the formula to determine the response needed to provide the best sound quality.

When looking at uses for prime numbers, I realized that prime numbers are used in computers, and they can be used to create extensive codes that are more difficult to break. It really is amazing how math affects us every day. Consumers neglect the fact that math goes into many of the products that we use or products that affect us in some way.

References

Bluman, A. (2005). Mathematics in Our World. United States of America: McGraw-Hill.

quadratic equation. (n.d.) The American Heritage® Dictionary of the English Language, Fourth Edition. (2003). Retrieved April 29 2011 from

http://www.thefreedictionary.com/quadratic+equation

prime number. (n.d.) The American Heritage® Dictionary of the English Language, Fourth Edition. (2003). Retrieved April 29 2011 from

http://www.thefreedictionary.com/prime+number