Best Inequality Questions For SBI PO And Clerk
In quadratic Equations, We have the following options to choose from:-
- X >Y
- Y >X
iii. X >= Y
- Y>= X
- X = Y or relationship cannot be established.
(i) Now, Suppose on solving the quadratic equation we get X = -1, 2 And Y = -2, -3
On putting these values on the number line we will see that X lies on the right of Y. Hence, We can say that X>Y or Y<X.
(ii) Now, Suppose if after solving the equation we get X = -1, 2 and Y= 3,4.
On putting these values on the number line we see that Y lies to the right of X without touching X at any point. Hence, We can say that Y>X or X<Y.
(iii) If X= 3,4 and Y= 2,3. Putting this on the number line we get X to the right of Y but touching Y at one single point i.e., 3. Hence, X>=Y or Y<=X.
(iv) If X=3,4 and Y=4,5. Putting these values on the number line we will see that Y lies to the right of X but touching X at 4. Hence, Y>=X or X<=Y.
(v) Now, Suppose X= 2,4 and Y= 3,5. Putting these values on the number line we will see that X touches Y at all the points between 3 and 4 i.e., at 3, 3.1, 3.2, 3.3, etc. up to 4 hence, in this case we cannot relate X and Y and Hence, Will answer as Relationship cannot be established.
Also, suppose if y=7 and X= 4,8 then X<y also X> y. Hence, in this case, also no relationship can be established.
Example some quadratic equation:
(i) 6X^2 +11X + 3 = 0
(ii) 6X^2 + 10X +4= 0
(i) Shortcut tricks :
This equation +6 is coefficient of x2 . + 11 is coefficient of x
+3 is constant term.
Step 1: we multiply (+6) x (+3) = +18 = 2x3x3
Step 2: we break 2x3x3 in two parts such that addition between them is 11.
So, 2x3x3 = 2 x 9. Also, 9 +2 = 11
So , +9 and +2 = Sum of is +11 .
Step 3: Change the sign of both the factors , So +9 = -9 and +2 = -2 .
and divide by coefficient of x2 , So we get -9 / 6 = -3 / 2 and -2 / 6 = – 1 / 3 .
Therefore, X = -3/2 , -1/3
Similarly Solving (ii),
6×4= 24 = 2x2x2x3
Break 2x2x2x3 into two parts such that their sum becomes 10.
2×2 and 2×3 are two parts of 24 whose sum is 10.
Now, Change the sign of both the factors and divide by coefficient of X^2.
So, +4 = > -4/6
And +6 = > -6/6
Y = –2/3 , -1
So, in all X= -1.5, -0.33
And, Y = -0.667, -1
Now, Putting these values on Number line we get to knw that from -0.667 to -1
The values of X and Y coincides .
Hence, as X and Y coincide at more than 1 point,
We can Say X=Y or Relationship between X and Y cannot be established.
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