Home > Math Shortcuts > Single variable Quadratic equations

Single variable Quadratic equations shortcut tricks are very important thing to know for your exams. Time takes a huge part in competitive exams. If you know how to manage time then you will surely do great in your exam. Most of us miss this thing. Here in this page we give few examples on Single variable Quadratic equations shortcut tricks. All tricks on single variable quadratic equations are provided here. Visitors please read carefully all shortcut examples. You can understand shortcut tricks on Single variable Quadratic equations by these examples.

Before doing anything we recommend you to do a math practice set. Write down twenty math problems related to this topic on a page. Solve first ten math problems according to basic math formula. You also need to keep track of the time. After solving all ten math questions write down total time taken by you to solve those questions. Now practice our shortcut tricks on single variable quadratic equations and read examples carefully. After finishing this do remaining questions using Single variable Quadratic equations shortcut tricks. Again keep track of Timing. The timing will be surely improved this time. But this is not enough. You need to practice more to improve your timing more.

### Few Important things to Remember

We all know that the most important thing in competitive exams is Mathematics. That doesn’t mean that other topics are less important. You can get a good score only if you get a good score in math section. A good score comes with practice and practice. All you need to do is to do math problems correctly within time, and this can be achieved only by using shortcut tricks. But it doesn’t mean that without using shortcut tricks you can’t do any math problems. You may have that potential to do maths within time without using any shortcut tricks.

But, other peoples may not do the same. Here we prepared single variable quadratic equations shortcut tricks for those people. Here in this page we try to put all types of shortcut tricks on Single variable Quadratic equations. But if you see any tricks are missing from the list then please inform us. Your little help will help so many needy.

In single quadratic equation has maximum power of unknown variable has two.In maths exam papers there are two or three question are given from this chapter.This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam. Under below  given some more example for your better practice.

Example:

ax2 + bx + c = 0

It is equal to 0 and the a, b, c are the constant value and we can say that x represent as unknown.
The a, b, c are the constant and quadratic coefficient or linear coefficient. Quadratic equation hold the only power of x which is also non negative integer.

### How to solve the Single Variable Quadratic Equations

4x2 + 12x + 8 = 0

This equations contain 4x2 and 12x where positive +4 is the coefficient of x2 and 12x where positive +12 is contain coefficient of x and 8 is constant variable.

1. First we multiply the positive +8 and positive +4 that is 32.
2. We separate 32 into 8 and 4 which is a addition result of 12 and 12 we get addition of 8 and 4.
3. Switch the sign the both factors number, that is, +8 into -8 and +4 into -4.
4. Divide by the coefficient of x2, that is 4. So, -8 / 4 and -4 / 4.
5. Result we get is x = -2 and -1.

### Example #1 – Single variable Quadratic equations

x2 + 9x + 20 = 0

1. -3 and -2
2. -4 and -3
3. -5 and -4
4. -6 and -4

Show Answer Show How to Solve Open Rough Workspace

How to Solve
5 x 4 = +20
We break +20 in two parts such that addition between them is 9.
+20 = (+5) + (+4) = +9 .

Change the sign of both the factor and divide by coefficient of x2, that is 1.
So, -5 / 1 = -5, and
-4 / 1 = -4.

Rough Workspace

### Example #2 – Single variable Quadratic equations

y2 + 13y + 28 = 0

1. -7 and -4
2. -6 and -4
3. -5 and -3
4. -4 and -3

Show Answer Show How to Solve Open Rough Workspace

How to Solve
7 x 4 = +28
We break +28 in two parts such that difference between them is 3.
+28 = (+7) – (+4) = +3.

Change the sign of both the factor and divide by coefficient of y2, that is 1.
So -7 / 1 = -7, and
-4 / 1 = -4.

Rough Workspace

### Example #3 – Single variable Quadratic equations

4y2 + 12y + 8 = 0

1. -3 and -2
2. -2 and -1
3. -4 and -3
4. -5 and -2

Show Answer Show How to Solve Open Rough Workspace

How to Solve
4 x 8 = +32
We break +32 in two parts such that addition between them is 12.
+32 = (+8) + (+4) = +12.

Change the sign of both the factor and divide by coefficient of y2, that is 4.
So, -8 / 4 = -2, and
-4 / 4 = -1.

Rough Workspace

Example #4

6x2 + 10x + 4 = 0

1. -4 and -5/6
2. -3 and -4/5
3. -2 and -3/4
4. -1 and -2/3

Show Answer Show How to Solve Open Rough Workspace

How to Solve
6 x 4 = +24
We break +24 in two parts such that addition between them is 10.
+32 = (+6) + (+4) = +10.

Change the sign of both the factor and divide by coefficient of x2, that is 6.
So, -6 / 6 = -1, and
-4 / 6 = -2 / 3.

Rough Workspace

### Few examples of Inequality with Shortcut Tricks

If you have any question regarding this topic then please do comment on below section. You can also send us message on facebook.

1. akshit singla says:

sir how to solve equation in which coefficient of x is negative??

2. Bhushan Dafale says:

4y2 + 12y + 8 = 0……….use html superscript tag like

4y2 + 12y + 8 = 0……….plz explain my question

x2+9x+20=0….ans: x=-5 , x=-4……..u gave x=-1/5, x=-1/4

3. Bhushan Dafale says:

4. 5. 