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## 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:____Example 1:__

(i) 6X^2 +11X + 3 = 0

(ii) 6X^2 + 10X +4= 0

__Answer :____(i) Shortcut tricks :__

This equation +6 is coefficient of x^{2} . + 11 is coefficient of x

+3 is constant term.** Step 1:** we multiply (+6) x (+3) = +18 = 2x3x3

**we break 2x3x3 in two parts such that addition between them is 11.**

__Step 2:__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 x

^{2}, 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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