QUADRATIC EQUATION FOR IBPS CLERK PRE
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Directions (Q. 1 - 10): In each of these questions, two equations (I) and (II) are given. You
have to solve both the equations and give answer
1) if x > y
2) if x > y
3) if x < y
4) if x < y
5) if x = y or relationship between x and y cannot be established
1. I. 4x + 7y = 42
II. 3x – 11y = –1
2. I. 9x2 – 29x + 22 = 0
II. y2 – 7y + 12 = 0
3. I. 3x2 – 4x – 32 = 0
II. 2y2 – 17y + 36 = 0
4. I. 3x2 – 19x – 14 = 0
II. 2y2 + 5y + 3 = 0
5. I. x2 + 14x + 49 = 0
II. y2 + 9y = 0
6. I.7x2 – 9x + 2 = 0
II. y2 – 4y + 3 = 0
7. I. x2 = 64
II. 2y2 + 25y + 72 = 0
8. I.x2 + x – 20 = 0
II. 2y2 – 19y + 45 = 0
9. I.7x + 3y = 26
II. 2x + 17y = – 41
10. I.3x2 – 20x + 33 = 0
II. 2y2 – 11y + 15 = 0
ANSWERS:
1. 1; eqn (I) ×3 – eqn (II) × 4
12x  21y  126
12x – 44y  – 4
– 

65y  130
y = 2 and x = 7
2. 3; I. 9x2 – 18x – 11x + 22 = 0
or, 9x(x – 2) – 11(x – 2) = 0
or, (x – 2) (9x – 11) = 0
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x = 2,
11
9
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II. y2 – 3y – 4y + 12 = 0
or y(y – 3) – 4(y – 3) = 0
or (y – 3) (y – 4) = 0
y = 3, 4
x<y
3. 4; I. 3x2 – 4x – 32 = 0
or 3x2 – 12x + 8x – 32 = 0
or 3x(x – 4) + 8(x – 4) = 0
or (3x + 8) (x – 4) = 0
8
3
x = 4, –
II. 2y2 – 8y – 9y + 36 = 0
or 2y(y – 4) – 9(y – 4) = 0
or (2y – 9) (y – 4) = 0
or (2y – 9) (y – 4) = 0
9
2
y = 4,
x < y
4. 1; I. 3x2 – 21x + 2x – 14 = 0
or 3x(x – 7) + 2(x – 7) = 0
or (3x + 2) (x – 7) = 0
x = 7, –
2
3
II. 2y2 + 5y + 3 = 0
or 2y2 + 2y + 3y + 3 = 0
or 2y(y + 1) + 3(y + 1) = 0
or (2y + 3) (y + 1) = 0
y =
–
3
2
, –1
x > y
5. 5; I. x2 + 14x + 49 = 0
or (x + 7)2 = 0
x+7=0
or,x = –7
II. y2 + 9y = 0
or y(y + 9) = 0
y = 0, –9
ie no relation between x and y.
6. 4; I. 7x2 – 7x – 2x + 2 = 0
or,7x(x – 1) –2(x – 1) = 0
(7x – 2) (x – 1) = 0
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or,x =
2
7
,1
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II. y2 – y – 3y + 3 = 0
or,y(y – 1) –3(y – 1) = 0
or,(y – 3) (y – 1) = 0
 y = 1, 3
xy
7. 5;I.x2 = 64
x = ±8
II.2y2 + 9y + 16y + 72 = 0
or,y(2y + 9) + 8(2y + 9) = 0
or,(y + 8) (2y + 9) = 0
 y = –8,

9
2
i.e, no relation between x and y.
8. 3;I.x2 + x – 20 = 0
or,x2 + 5x – 4x – 20 = 0
or,x(x + 5) –4(x + 5) = 0
or,(x – 4) (x + 5) = 0
 x = 4, – 5
II.2y2 – 10y – 9y + 45 = 0
or,2y(y – 5) –9(y – 5) = 0
or,(y – 5) (2y – 9) = 0
y = 5,
9
2
x<y
9. 1;Eqn (I) × 2
Eqn (II) × 7
14x  6y  52
14x  119y  287
__________
_______
 

113y  339
 y = –3 and x = 5, ie x > y
10. 2;I.3x2 – 9x – 11x + 33 = 0
or,3x(x – 3) – 11(x – 3) = 0
or,(3x – 11) (x – 3) = 0
x = 3,
11
3
II.2y2 – 6y – 5y + 15 = 0
or,2y(y – 3) –5(y – 3) = 0
or,(y – 3) (2y – 5) = 0
y = 3,
5
2
xy
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