Inequality : Quadratic Equation For Bank PO

Hello Readers,
            Today we're going to learn another important topic for quant. Promise me If you'll master this trick you'll certainly ensure 5 marks out of 5 question in not more than 4 min. and if u really master this trick it will not going to take more than 3 min.

So first of all lets take a look at the questions how they are look alike :
 ax² + bx + c = 0
 py² + qy + s = 0
Now we need to find reletion between X and Y

The conventional method to solve these equation is either make their pairs of multiples or using Shridharacharya's formula we're going to use both of them but in a way it became lot more easier and less time consuming .

ok ! before we learn the trick first of all try to solve these equations with conventional method

3x²-6x+3 = 0
3y²+5y+2 = 0
(i) here a=3, b=-6 and c=3
first we multiply a by c, 3 x 3 = 9
now find multiple of 9 that will gives us 6 in either "adding" or "substracting" 
like , -3 - 3 = -6
now divide equation like 
     3x²-3x-3x+3 = 0
=  3x(x-1)-1(x-1) = 0
=  (3x-1)(x-1) = 0
=  x= 1/3     AND   x = 1
similarly
3y²+5y+2 = 0
here, a=3,b=5 c=2
now a*c = 3*2 = 6
now lets find factors of 6 that will gives us 5 on either adding or substracting
which is 3 and 2
3y²+5y+2 = 0
3y²+3y+2y+2 = 0
3y(y+1)+2(y+1)=0
(3y+2)(y+1)=0
y= -2/3    AND   y=-1

Finally we have x=1/3 , 1
and y= -2/3 , -1
here both values of x is +ve(positive)
and that of y is -ve(negetive )
hence x>y

Now lets do the same question using Short Trick:
First of all remember These Signs 

here as you can see + + (these are sign of b and c of quadratic equation ) converted into - - 
Take a look at the example to understand better 
3y²+5y+2 = 0
a=3, b= +5 , c= +2 
and as we seen earlier solution will gives as
y = - 3 , y= -2
hence once we remember those sign conversions we did the half done.
In the above example We can deduce the ans without even solving the equations 
EX.1 3x²-6x+3 = 0
        3y²+5y+2 = 0 

Sol: Here first equation is converted as
x = - + = + +(hence both roots of x will be positive)
and 
y= + + = - -(hence both roots of y will be negetive)
so we can say  x>y
Try these Questions :



Next Step :
x²+x+12 = 0 a=1, b= +1 ,c =+12
y²+2y+15 = 0 a=1, b= +2 ,c =+15
Now First Step Is to Find Sign of both equations 
here x= + + = - -
and y=  + + = - - 
Now,solving for x
multiply a by c = 12
find roots of 12 = 4*3 
now put the larger value at first place and smaller at other
Like this -4, -3
Similerly Solving For y
Multiply a by c = 15 
factors of 15 that will gives 2 on adding or multiplying = 5 * 3
finally putting the larger value in the first sign and smaller into the other
- 5, -3
hence both the values
x=  -4, -3
y= -5, -3

Got Any Doubt post at comments below