Home MATHEMATICS TOPIC 3: QUADRATIC EQUATIONS ~ MATHEMATICS FORM 2

TOPIC 3: QUADRATIC EQUATIONS ~ MATHEMATICS FORM 2

3852
480

TOPIC 3: QUADRATIC EQUATIONS ~ MATHEMATICS FORM 2

Solving quadratic equations can be difficult, but luckily there are several different methods that we can use depending on what type of quadratic that we are trying to solve.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

The standard form of a Quadratic equation is ax2 + bx + c =0whereby abc are known values and ‘a’ can’t be 0. ‘x’ is a variable (we don’t know it yet). a is the coefficient of x2 , b is the coefficient of x and c is a constant term. Quadratic equation is also called an equation of degree 2 (because of the 2 on x). There are several methods which are used to find the value of x. These methods are:

1. by Factorization
2. by completing the square
The Solution of a Quadratic Equation by Factorization
Determine the solution of a quadratic equation by factorization
We can use any of the methods of factorization we learnt in previous chapter. But for simplest we will factorize by splitting the middle term. For Example: solve for x, x2 + 4x = 0
solution Since the constant term is 0 we can take out x as a common factor.

So, x2 + 4x = x(x + 4) = 0. This means the product of x and (x + 4) is 0. Then, either x = 0 or x + 4 = 0. If x + 4 = 0 that is x = -4. Therefore the solution is x = 0 or x = -4.

Example 1

Solve the equation: 3x2 =- 6x – 3.
first rearrange the equation in its usual form.
that is:
3x2 = – 6x – 3
3x2 + 6x + 3 = 0
now, factorize the equation by splitting the middle term. Let us find two numbers whose product is 9
and their sum is 6. The numbers are 3 and 3. Hence the equation 3x2 + 6x + 3 = 0 can be written as:
3x2 + 3x + 3x + 3 = 0
3x(x + 1) + 3(x + 1) = 0
(3x + 3)(x + 1) (take out common factor which is (x + 1))
either (3x + 3) = 0 or (x + 1) = 0
therefore 3x = -3 or x = -1
x = -1 (divide by 3 both sides) or x = -1
Therefore, since the values of x are identical then x = -1.

Example 3

solve the following quadratic equation by factorization: 4x2 – 20x + 25 = 0.
Solution
We need to split the middle term by the two numbers whose product is 100 and their sum is -20. The numbers are -10 and -10.
The equation can be written as:
4x2 -10x – 10x + 25 = 0
2x(2x – 5) – 5(2x -5) = 0
(2x – 5)(2x – 5) (take out common factor. The resulting factors are identical. This is a perfect square)
since it is a perfect square, then we take one factor and equate it to 0. That is:
2x – 5 = 0
2x = 5 then, divide by 2 both sides.

Therefore

Example 4

solve the equation x2 – 16 = 0.
Solution
We can write the equation as x2 – 42 = 0. This is a difference of two squares. The difference of two squares is an identity of the form:
a2 – b2 = (a – b)(a + b).
So, x2 – 42 = (x – 4)(x + 4) = 0
Now, either x– 4 = 0 or x + 4 = 0
Therefore x = 4 or x = -4

The Solution of a Quadratic Equation by Completing the Square

Find the solution of a quadratic equation by completing the square

Completing the square.

Example 5
Add a term that will make the following expression a perfect square: x2 – 8x
find a term that must be added to make the following expression a perfect square: x2 + 10x
Example 6
solve the following quadratic equation by completing the square: x2 + 4x + 1 = 0
Example 7
solve by completing the square: 3x2 + 7x – 6 = 0

1. Having read this I thought it was really informative. I appreciate you taking the time and effort to put this content together. I once again find myself spending way too much time both reading and commenting. But so what, it was still worthwhile!

2. Hello there! This is my first visit to your blog! We are a collection of volunteers and starting a new initiative in a community in the same niche.Your blog provided us beneficial information to work on. Youhave done a marvellous job!

3. I enjoy what you guys are usually up too. This type of clever work and exposure!Keep up the superb works guys I’ve incorporated you guys to my blogroll.

4. Olá! Publiquei um trecho de 24 segundos para divulgar o novo clipe da Juliette e ele foi bloqueado. Vocês me ajudam? Vocês me autorizam? Foi no meus Reels no @popluvbrasil no Instagram.

5. Normally I do not learn post on blogs, however I wouldlike to say that this write-up very compelled me to try and doit! Your writing taste has been amazed me. Thank you, quite great post.

6. Heya i抦 for the first time here. I found this board and I find It really useful & it helped me out much. I hope to give something back and aid others like you aided me.

7. Thanks for the marvelous posting! I really enjoyed reading it, you are a great author.I will be sure to bookmark your blog and may come back in the foreseeable future.I want to encourage you continue your great posts,have a nice morning!

8. Generally I don’t read article on blogs, but I wish to say that this write-up very compelled me to check out and do it! Your writing style has been amazed me. Thank you, very nice article.

9. Herkes bol takipçi ister, size en yüksek miktarlarda takipçi atacak ve en cüzi fiyattan instagram takipçi satın almanıza yarayacak panelimiz hızlıdır.

10. I am not certain where you’re getting your info, but great topic. I needs to spend some time learning more or figuring out more. Thanks for magnificent information I was looking for this information for my mission.

11. On the other hand, betting on high college athletic eventsremains illegal.

12. Attractive section of content. I just stumbled upon your blog and in accession capital to assert that I acquirein fact enjoyed account your blog posts. Anyway I will be subscribing to your feeds andeven I achievement you access consistently quickly.