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# Quadratic equations

## Quadratic equations

Shortcut Tricks are very important things in competitive exam. Time is the main factor in competitive exams. If you know how to manage time then you will surely do great in your exam. Most of us skip that part. Few examples on quadratic equations shortcuts is given in this page below. All tricks on quadratic equations are provided here. We request all visitors to read all examples carefully. These examples will help you to understand shortcut tricks on Quadratic equations.

Before starting anything just do a math practice set. Write down twenty math problems related to this topic on a page. Do first ten maths using basic formula of this math topic. You also need to keep track of the time. After finish write down total time taken by you to solve those ten maths. Now read our examples on quadratic equations shortcut tricks and practice few questions. After this do remaining ten questions and apply shortcut formula on those math problems. Again keep track of Timing. You will surely see the improvement in your timing this time. But this is not all you need. You need more practice to improve your timing more.

### Few Important things to Remember

Math section in a competitive exam is the most important part of the exam. It doesn’t mean that other topics are not so important. You can get a good score only if you get a good score in math section. You can get good score only by practicing more and more. All you need to do is to do math problems correctly within time, and this can be achieved only by using shortcut tricks. Again it does not mean that you can’t do maths without using shortcut tricks. You may have that potential to do maths within time without using any shortcut tricks. But other peoples may not do the same. So Quadratic equations shortcut tricks here for those people. We try our level best to put together all types of shortcut methods here. But if you see any tricks are missing from the list then please inform us. Your little help will help others.

### Quadratic Equation

In a mathematical calculation, a quadratic equations is came from the Latin word that is quadrature’s which is called square is a structure. 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.

### Example #1

6x2 +11x + 3 = 0

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

Show Answer Show How to Solve Open Rough Workspace

Answer: Option (C)
How to Solve
In this equation +6 is coefficient of x2.
+ 11 is coefficient of x.
+3 is constant term.

Now, we multiply (+6) x (+3) = +18
Then, we break +18 in two parts such that addition between them is 11.
+18 = 9 + 2 = 11, and product of both factors is 18.

So , +9 and +2 = Sum of it is +11.

Change the sign of both the factors , So +9 = -9 and +2 = -2.
Now, divide by coefficient of x2,
So, we get,
-9 / 6 = -3 / 2, and
-2 / 6 = -1 / 3.

Rough Workspace

### Example #2

4y2 + 12y + 8 = 0

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

Show Answer Show How to Solve Open Rough Workspace

Answer: Option (A)
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 sign of both factor and divide by coefficient of y2,
So, we get,
– 8 / 4 = -2.
– 4 / 4 = -1.

Rough Workspace

### Example #3

x2 + 10x + 4 = 0

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

Show Answer Show How to Solve Open Rough Workspace

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

Change sign of both factor and divide by coefficient of x2,
So, we get,
– 6 / 6 = -1.
– 4 / 6 = -2 / 3.

Rough Workspace

### Example #4

x2 + 9x + 20 = 0

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

Show Answer Show How to Solve Open Rough Workspace

Answer: Option (B)
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 sign of both factor and divide by coefficient of x2,
So, we get,
– 5 / 1 = -5.
– 4 / 1 = -4.

Rough Workspace

### Example #5

3y2 + 19y + 28 = 0

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

Show Answer Show How to Solve Open Rough Workspace

Answer: Option (C)
How to Solve
3 x 28 = +84
We break + 84 in two parts such that difference between them is 19.
+84 = (+12) + (+ 7) = +19 .

Change sign of both factor and divide by coefficient of y2, that is 3.
So, we get,
y = -12 / 3 = -4.
y = -7 / 3 = – 7 / 3.

Rough Workspace

### Few examples of Inequality with Shortcut Tricks

So, here we provide few shortcut tricks on this topic. Please visit this page to get updates on more Math Shortcut Tricks. You can also like our facebook page to get updates.

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## 42 comments

1. prashant says:

good techniques are given to to solve quadratic equations but found many mistakes… pls make it correct!!!

• Admin says:

thank u prashant for your feedback pls mention the page where u dont understand and found mistakes ….

• christy says:

Very useful…like it..thanks.

• Akshay says:

i did not find any mistakes in it but the problems are of elementary sort. in my country even children can solve them easily. the problems arise when they start putting up difficult questions. so it would be very kind of you if you could complete the lecture by inclusion of mind binding problems. i think by applying the differentiation method on these problems we get rid of such difficulties

• jaytin says:

I found it correct

2. Bhushan Dafale says:

Please explain Example 4.

probably final values are x=-5 and x=-4 ….

3. sagar pandagre says:

sir pls give some SBI po and RBI quadratic equation which are tough to solve and how to compare them

• Admin says:

both are tough but not impossible to solve, do practice more on basics…

4. rajesh says:

very helpfull…thnx alot sir

5. madhura says:

very useful …thank you

6. anuparno says:

ok i have a question :
1.x^2-x-2=0 and 2.y^2+5y+6=0
now after solving i get x=+4,-3 and y=-3,-2 so there is 1 common value -3 and other value of x is greater thn y so answer should be x>=y
but answer is relation cant be established how cn it be possible is any concept is here??

• Aditi says:

Sir we need to compare both values of x with both values of y.
I mean to say +4 is greater than both values of y, but -3 is not greater than -2 ,so ans is relation can’t be established. I hope u understood.

• pankaj says:

x^2-x-2=0. y^2+5y+6=0
x^2-2x+x-2=0. y^2+6y-y+6=0
x(x-2)+1(x-2)=0. y(y+6)-1(y+6)=0
(x+1)(x-2)=0. (y-1)(y+6)=0
x=-1,2 y=1,-6.

x>y

• lol says:

if y ‘s value is within the value of x then no relation

• sri says:

first equation roots are 2,-1 not 4, 3 and 2 nd eq roots -3,-2 so there is no relation

• asha says:

x=-1,2 , y= -3,-2
by comparing can’t we say y<x ?

7. saranya says:

xsquare is equal to 25 means then the answer is +or-5….the SAME WAY xpower4 is equal to 625 means wat is the x value? +or-5 ya or +5 only ya????please reply me…

8. Aman says:

and what about negTive values

9. balveer says:

Nice trick

10. Aparajita Srivastava says:

Thanks for sharing these short cut technique but it will be good if you sharing some more question where equations are in negative like x2-x-2=0
so that we won’t get confuse in sign.

11. Shubh says:

NY question is x²+5x-6.
according to the above said method, a×c = 1×6=6
6 can be broken in two ways to be equal to mid term 5 as :
6×1 = 6 and 6-1= 5………………(way 1).
and also
2×3 = 6 and 2+3= 5………………(way 2).

Assuming that I follow this short trick and not solving this equation by the traditional long cut method, as there will be no time to do so & check every equation,

if I go way 1 i get x = 1, -6.
while,
if I go way 2 i get x = -3, -2.

then how do I know which way should I go.. way 1 or way 2?… as both appear to be right in the short cut method!!!

• akhil says:

You have to make the product of -6 which is not there in your second values i.e 2×3. So only values 6 X -1= -6 & 6 -1 =5 is valid.

• Sidhartha says:

x^2+5x-6
=x^2+6x-x-6
=x(x+6)-1(x+6)
=(x-1)(x+6)
x=1 and x=-6
shortcut
-6/1=-6 and 1/1=1
and remember one thing sum of 2x and 3x can be 5x bt product cant be -6

12. sanyog says:

thnk u vry mch sir.. this is vry helpful

13. ganesh nayak says:

excellent tricks,this lots helps to bank aspirents

14. Kalpana says:

Sir can you please tell me how to compare values of x and y. Especially the cases where relation between both variable can not be established.

15. jaytin says:

Bestest trick I found on net.thanxxxxxxxx

16. sh says:

thanks from bottom of my heart

• Admin says:

welcome, and keep visiting.

17. sarbjeet says:

11x^2-240x-44=0
plz solve this with explanation

18. sarbjeet says:

11x^2-240x-44=0 plz solve

19. Satyam Negi says:

Is there any other way of solving these questions specially when the coefficients are very large. With this method the calculation for such questions will become so hectic. So are there any other way to deal with that kind of problems?

20. Radha says:

How to use shortcut for big values like 9*20 cums 180 . how to divide it for 27.

21. Narender Arya says:

Sir/Madam

Plz help me in this type of question

5x^2-87x+378=0
3y^2-49y+200=0

X>y
X=y
x<=y
No any relation being established.

Plz help me..

22. satnam says:

I’m confuse here.
we break + 24 in two parts such that addition between them is 10.
+24 = (+6) + (+ 4) = +10 .
I can’t understand it. It’s how..¿¿¿

23. Rocky says:

It’s just a regular technique… Don’t again say that this is a shortcut, it’s really waste of time

24. Manoj says:

Superb technique in simple way , loved it simply awesome sir .

25. Musty Mohammed says:

Interesting sir we highly appreciate

Buh sir am having problem with with quatic equations lke

6x^4-35x^3+6x^2-35x+6

Sir please if there’s any tricky way

26. Musty Mohammed says:

Sir cubic equation and quartic

27. Ridwan says:

thank you for the shortcuts i really appreciate
but I have a question to ask

what if the product of the co-efficient of x^2 and the constant is much pls explain to us hw we can easily get d 2 numbers dat can b multiplied to give the product and can be added to give the co-efficient of x

28. Rah says:

Not able to understand example 3