What's the best way to solve a quadratic equation?

Question

We're having a test on the quadratic equation, and I need to know what you think is the best and easiest way to solve one of these annoying problems. Also, are there any other methods?

Oh yeah, and there's a bonus question on making your own quadratic equation using completing the square. Anyone know how to do this?

Answer 1

i think the best way to solve a quadratic equation is by factorising it (if possible).

eg1. x^2 + 6x + 5 = 0
(x + 1)(x + 5) = 0
so x = -1 or x= -5

Or if you are allowed a calculator then you could just use the quadratic formula.

ax^2 + bx + c = 0
x= (-b plus or minus the square root of ( (-b)^2 - 4(a)(c) ) )
all divided by 2a

completing the square is also easy if the coefficient of
x squared is 1. If not, you should probably use the formula..

Answer 2

It seems that everyone is focusing on the first half of your question and ignoring the part about completing the square, so I'm ONLY going to address that second part.

I'll show you how using the earlier example of
x^2 + 6x +5 = 0
[x^2 + 6x +(6/2)^2] - (6/2)^2 +5 = 0
(x + 3)^2 - 9 + 5 = 0
(x + 3)^2 = 4
sqrt(x + 3)^2= =/- sqrt(4)
x+3 = +/- 2

So, if x+3 = 2
then x = -1

and if x+3 = -2
then x = -5

The generalized version of completing the square (using ax^2 + bx + c = 0) will result in the quadratic formula, so I won't type it out here -- just look up the deriving the quadratic formula in your textbook.

Answer 3

Best method to solve quadratic equations.
The first obvious choice is the quadratic formula since it can solve any quad. equation in standard form ax^2 + bx + c by using calculators. However, there are exceptions and inconveniences:
- Solving by formula always feels tedious and boring and that is not the the goal of learning math. Its ultimate goal aims to improve logical thinking and deductive reasoning of students. That is why. math curriculum wants students to learn other more solving methods.
- Using the quadratic formula requires students to remember by heart the formula and to know how to extract the square root of a number when calculators are not allowed, in some tests/exams, for example.
- In some cases,it is simpler and faster using other solving methods, such as the factoring AC Method or the new Diagonal Sum Method.
- The class instructions want students to solve quad. equations by other methods.

When the given quad. equation in standard form ax^2 + bx + c = 0 can be factored, there are 2 best
methods to solve it.
1. The factoring AC Method that factors the equation into 2 binomials in x. Then, it solves the 2 binomials for x.
NOTE. Recently, a "new and improved factoring AC Method" was introduced by the author, Nghi H Nguyen (Google Search or Yahoo Search). The improved method makes the solving approach simpler and faster.
2. The new Diagonal Sum Method that directly find the 2 real roots in the form of 2 fractions. You may read the method in articles titled:"Solving quadratic equations by the Diagonal Sum Method" on Google or Yahoo Search.

Answer 4

the best way to solve the quadratic equation is to use the quadratic formula..
yes..there are other methods like factoring, completing the square, etc., but the simplified form of these methods is the quadratic formula..

Answer 5

The best way depends on the actual equation. The most dependable way would be using the quadratic formula. However factoring is much more efficient on factorable equations.

Answer 6

By factorising :

eg1. x^2 + 6x + 5 = 0
(x + 1)(x + 5) = 0
so x = -1 or x= -5

Or just use the quadratic formula:

ax^2 + bx + c = 0
x= (-b plus or minus the square root of ( (-b)^2 - 4(a)(c) ) )
all divided by 2a

Answer 7

There are many ways to deal with a quadratic equation, it all depends on which method is best. For one, you can try factoring, completing the square, synthetic division and or the quadratic equation...

Answer 8

Easiest way of solving a quadratic equation is direct usage of the quadratic formula.

the other method is the perfect square method from which the formula can also be derived.

Answer 9

Use the general formula for solving quadratic equation:

For the equation:
ax² + bx + c = 0

x = [ -b ± SQRT(b² - 4ac) ] / (2a)

As you can see, 2 values for x may be obtained due to the ambiguous sign ±

Answer 10

quadratic formula

*sang to pop goes the weasle*

x is equal to negative b
plus or minus the square root
of b squared minus 4 ac
all over 2 a