Quadratics Made Easy

Solving Quadratic Equations

Let's have a look at how we solve a quadratic equation:

x²-3x+2=0

The easiest way to solve them is to follow certain steps:

Step 1

Find two numbers where when they are multiplied together equal the firstnumber (a=1) multiplied by the third number (c=2). These two numbers when addedto each other must also equal the second number (b=-3).

In the above example, the solution is -2 and -1.
We can see that when added together the result is -3 and that when multiplied together, the result is 2

Step 2

Rewrite the original equation splitting the middle part into two using thenumbers which you found in step 1.

x²-x-2x+2=0

Step 3

Start to factorise both halves of the equation:

x(x-1)-2(x-1)=0

At this point you will know if you are going along the correct track if thefirst bracket is the same as the second bracket.

Step 4

Collect everything before each bracket and put it into one bracket andmultiply this bracket by that which is inside the identical brackets:

(x-1)(x-2)=0

Step 5

In order for the left side of the equation to be equal to 0, one of the twobrackets must equal 0. So either:

a.
x-1=0
x=1

b
x-2=0
x=2

Step 6

Check these answers:

1²-(3*1)+2=0
1-3+2=0
0=0

2²-(3*2)+2=0
4-6+2=0
0=0

Therefore the possible solutions for the above equation are confirmed to be 1 and 2

Personal Learning Environments

Introduction. Metaphorically, it can be said that each individual human being is a self contained virtual world. The way I perceive life and the happenings in it are as specific to me as DNA and finger prints. This could be interpreted to say that the optimal method for me to learn is also somewhat unique and probably won’t match the next person. With developments in technologies and an understanding that traditional teaching doesn’t transpose to teaching online effectively with current techno

Systemic issues

(I know I haven’t written lately and this post is long. I’ll ask you to bear with me.) I used to think Don Brown was a pain in the ass. Those of you who are in NATCA, or familiar with ATC safety, know Don Brown. Those of you who aren’t but who are interested in ATC, or the FAA, or even if you’re not particularly interested and were just forwarded the link to this blog and occasionally fly on an airplane, or have friends/family who occasionally fly on airplanes, or if you ever get overnight pa

easy storybook

Apparently, my blog's reading level is a mere "elementary school"! Let's spice it up a little. In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be positive integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic curve or more general object, and ask about the lattice points on