Methods for Solving Quadratic Equations: Factorization, Formula, Completing Square, Study Guides, Projects, Research of Mathematics

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Math's

BC

ARRAN MORALEE

ASSIGNMENT 1

METHODS FOR

SOLVING EQUATIONS

TO A HIGHER

DEGREE

The way in which we solve quadratic equations depends upon the question in hand. For some equations, certain methods are better than others due to efficiency and the accuracy. However, when it comes to harder quadratics, we tend to use the more complex methods such as quadratic formulae or polynomial division. For the more simple methods, we can use a combination of factorisation, completing the square, and plotting a graph.

For this report, I have displayed the numbers on a piece of software, just for the look of things. It allows the reader to have a more focused reading when going through the report as it has no inaccuracies.

Factorising

Factorising tends to be done with more simple algebraic questions, and tends to be written in two different forms:

a(b+c) = ab+ac

(a+b)(c+d)= ac+ad+bc+bd

Therefor x = -2 OR -

X^2 = A

5X = B

6 = C

So...

A = x * x

B = b + d = 5

C = b * d = 6

Factorising can also be done with singular brackets, where there is a like term with the quadratic equation, and you can simply divide by that term which for this example, will be called ‘n’

For example - (4x+16) can be factorised with the like term being 4.

Dividing both terms by 4 will give a remaining (x+4)

The final factorised quadratic can be written like 4(x+4)

Quadratics

Quadratics can also be solved using the quadratic formula.

Form there, you + (b/2)^2 to both sides of the equation

Once the fractions have been simplified, you attempt to solve the equation for x, as you have x^2, you will always be left with a positive and a negative number, which in the end will leave you with two different numbers.

Simplifying and working the equation down gives you:

Which then simplifies to

As seen from above, the two results which were accumulated were both x = -2 and x= -3 which we know are both correct.

Graphing

Graphing the quadratic equation is as simple as it sounds. You take the x value, substitute it in to the equation, and that gives you the y value in the graph

When the graph has been plotted, you look to see where the graph has crossed the x axis. For this graph, the black dots show that the graph passed the x-axis at –3 and –2, which means that our x values were – and –3.

In conclusion, the five different methods for handling quadratic equations are all useful but are only used when they are needed. For example, it is much easier to put a quadratic equation in to the quadratic formula than to do a long polynomial division, even when it is a very long equation. For more simple and shorted equations, it is easier to just factorise them into separate brackets. The method which is chosen really depends upon the equation and the circumstance.

The software which is available for download can be found on h�ps://www.symbolab.com/.