Week 3 Assignment
MAT126- Survey of Mathematical Methods
July 2, 2012
Week 3 Assignment
Project # 1- I will attempt to solve quadratic equations using an interesting method which derived from India. Somebody (possibly in seventh-century India) was solving a lot of quadratic equations by completing the square. At some point, he noticed that he was always doing the exact same steps in the exact same order for every equation. Taking advantage of the one of the great powers and benefits of algebra (namely, the ability to deal with abstractions, rather than having to muck about with the numbers every single time), he made a formula out of what he'd been doing: (http://www.purplemath.com/modules/solvquad4.htm)
(A) X2 – 2x – 13 = 0
(a) Move the constant term to the right side of the equation
X2-2x-13 = 0
Add 13 to each side of the equation to move 13 to the right side
X2 - 2x – 13 + 13 = 0+13
X2 – 2x = 13
(b) Multiply each term in the equation by four time the coefficient of the x2 term.
Divide the coefficient of -2x by 2
-2/2 = -1
(c) Square the coefficient of the original x term and add it to both sides of the
Square the result
(-1)2 = 1
Add this value to each side of the equation. This means that you will add 1 to each side of the equation.
X2 - 2x + 1 = 13-1
X2 – 2x+1 = 14
The reason for moving the 13 to the right side of the equation, and then adding the 1 to each side of the equation is: Changing the left side of the equation so it can be factored as a perfect square.
X2 - 2x + 1 = 14
(x-1)(x-1) = 14
(x-1)2 = 14
(c) Take the square root of each side of the equation
(d) Take the square root of each side of the equation
√(x-1)2 = ± √(14)
x-1= ±√ (14)
Add 1 to each side of the equation to remove the 1 from the left side of the equation. This leaves the variablke x as the only term on the left side of the equation.
x = 1 ±√ (14)
(e) Set the left...