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25 October 2010

Solutions: Roots of a Quadratic Equation

In elementary mathematics, one will come across a polynomial equation of the second degree which are called quadratic equations.Here's the general form of a quadratic equation:

Where a ≠ 0 (The equation will become linear instead)

In high-schools, students are generally given the quadratic formula to solve the equation. The answer for the solved equation are called the roots of the quadratic equation. The solutions can be real or complex and there are two solutions to each quadratic equation.

The formula is given as:

Here, we will go through the derivations to the formula.

We begin as the standard form of a quadratic equation:

Moving the last term to the opposite side and dividing the terms with a;

By applying completion of squares;

rearranging the equation we finally get;


Anonymous said...

an even more interesting topic would be proving the basic addition, and subtraction. albeit i have to say it is a nice breather after your tedious essay

Anonymous said...

hello! just swing by to share my thoughts on your eye-opening essays.

Great, but can be improved:

1. some of them are not sufficiently detailed to make full sense.

2. I generally think you focused too much on the language rather than the physics (this makes a distinction between writer and researcher). This causes some fact to be rather... false. Eg:

"So, the star now started to fuse oxygen, lithium, and all the other elements in the familiar periodic table in your chemistry class into even heavier elements, now the star begin to feel heavy, literally."

Literally, you are implicating that the mass (or weight) of star is increasing. Is this true in our stellar model?

Try to improve. Like Anonymous, I'll be waiting for your next essay. Another topic to suggest would be the interpretation of quantum mechanics.

Anonymous said...

Hi. I think you have the completion of square wrong. The X should be "X", and not "X^2"