**Solved Quadratic Equations Asked in SBI Clerk**

**Quadratic Equations Asked in SBI Clerk Prelims 2018(23 June):**

**Question1) In the following question, there are two equations (I) and (II). Solve the equations and answer accordingly:**

**Give Answer:**

(a)x>y

(b)x<y

(c)x=y or relation can’t be established between x & y

(d)x≥y

(e)x≤y

**I.x**

^{2}– 5x + 6 = 0**II.y**

^{2}– 9y + 20= 0
Answer & Explanation:

Solve I.x

^{2}– 5x + 6 = 0
Or,x

^{2}– 5x + 6 = 0
Or,x

^{2}– 3x-2x + 6 = 0
Or,x(x – 3)-2(x – 3) = 0

Or,(x-2)(x – 3) = 0

X=2 or 3

Solve II.y

^{2}– 9y + 20= 0
Or, y

^{2}– 5y– 4y + 20= 0
Or,y(y – 5)-4(y – 5) = 0

Or,(y-5)(x – 4) = 0

y=5 or 4

Now, Compare x and y:

2<5 means x<y

2<4 means x<y

3<5 means x<y

3<4 means x<y

Therefore x<y is the correct answer.

**Question 2) In the following question, there are two equations (I) and (II). Solve the equations and answer accordingly:**

**Give Answer:**

(a)x>y

(b)x<y

(c)x=y or relation can’t be established between x & y

(d)x≥y

(e)x≤y

**I.6x**

^{2}– 11x + 4 =0**II.50y**

^{2}– 25y + 3 =0
Answer & Explanation:

Solve I.6x

^{2}– 11x + 4 =0
Or, 6x

^{2}– 8x-3x + 4 =0
Or, 2x(3x –4) -1(3x – 4) =0

Or, (2x -1)(3x – 4) =0

Or, x=1/2=0.5 or x=4/3=1.33

Solve II.50y

^{2}– 25y + 3 =0
Or, 50y

^{2}– 15y– 10y + 3 =0
Or, 5y(10y – 3)– 1(10y – 3) =0

Or, (5y– 1)(10y – 3) =0

Or,y=1/5=0.2 or y=3/10=0.3

Now, Compare x and y:

0.5>0.2 means x>y

0.5>0.3 means x>y

1.33>0.2 means x>y

1.33>0.3 means x>y

Therefore x>y is the correct answer.

**Question 3) In the following question, there are two equations (I) and (II). Solve the equations and answer accordingly:**

**Give Answer:**

(a)x>y

(b)x<y

(c)x=y or relation can’t be established between x & y

(d)x≥y

(e)x≤y

**I.x**

^{2}– 4x – 12 =0**II.y**

^{2}– 5y – 14 =0
Answer & Explanation:

Solve I.x

^{2}– 4x – 12 =0
Or, x

^{2}– 6x+ 2x – 12 =0
Or, x(x – 6) + 2(x – 6) =0

Or, (x + 2)(x – 6) =0

Or,x=-2 or 6

Solve II.y

^{2}– 5y – 14 =0
Or, y

^{2}– 7y+ 2y – 14 =0
Or, y(y – 7)+ 2(y –7) =0

Or, (y+ 2)(y –7) =0

Or,y=-2 or 7

Now, Compare x and y:

-2>-2 means x=y

-2<7 means x<y

6>-2 means x>y

6<7 means x<y

Therefore No relationship can be established because
>,< & = never occur together.

**Question 4) In the following question, there are two equations (I) and (II). Solve the equations and answer accordingly:**

**Give Answer:**

(a)x>y

(b)x<y

(c)x=y or relation can’t be established between x & y

(d)x≥y

(e)x≤y

**I.3x**

^{2}+ 8x + 4=0**II.6y**

^{2}+ 7y + 2 =0
Answer & Explanation:

Solve I.3x

^{2}+ 8x + 4=0
Or, 3x

^{2}+ 6x+ 2x + 4=0
Or, 3x(x + 2) + 2(x + 2)=0

Or, (3x + 2) + (x + 2)=0

Or, x=-2/3=-0.66 or x=-2

Solve II.6y

^{2}+ 7y + 2 =0
Or, 6y

^{2}+ 4y + 3y + 2 =0
Or, 2y(3y + 2) +1( 3y + 2) =0

Or, (2y+1)( 3y + 2) =0

Or,y=-1/2=-0.5 or y=-2/3=-0.66

Now, Compare x and y:

-0.66>-0.5 means x<y

-0.66=-0.66 means x=y

-2>-0.5 means x<y

-2<-0.66 means x<y

Therefore x≤y is the correct answer.
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