## Algebra For SBI PO : Set – 22

D.1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

1) I. 2x2 + 13x – 7 = 0

II. 2y2 – 5y + 3 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(c)

2x2 + 13x – 7 = 0

or 2x2 + 14x – x – 7 = 0

or 2x (x + 7) – 1 (x + 7) = 0

or (2x – 1) (x + 7) = 0

∴x=1/2, -7

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=1,3/2

Hence x < y

2) I. 2x2-15x + 28 = 0

II) 4y2 – 16y + 15 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(a)

2x2 – 8x – 7x + 28 = 0

or 2x (x – 4) – 7(x – 4) = 0

or (2x – 7) (x – 4) = 0

4y2 – 16y + 15 = 0

or 4y2 – 6y – 10y + 15 = 0

or 2y (2y – 3) – 5(2y – 3) = 0

or (2y – 5) (2y – 3) = 0

∴y=5/2,3/2

Hence x > y

3) I. x2 + 8x + 16 = 0

II) y2 = 16

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(d)

x2 + 8x + 16 = 0

or (x + 4)2 = 0

or x + 4 = 0

x = -4

II. y2 = 16

y = ±4

4) I. x2 – 2x – 24 = 0

II) y2 + 8y = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(e)

x2 – 2x – 24 = 0

or x2 + 4x – 6x – 24 = 0

or x(x + 4) – 6(x + 4) = 0

or (x – 6) (x + 4) = 0

x = 6, – 4

II. y2 + 8y = 0

or y(y + 8) = 0

y = 0, – 8 ie No relation can be established between x and y.

5) I. x2 + 4x = 0

II) y2 + 10y + 25 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(a)

x2 + 4x = 0

or x(x + 4) = 0

x = 0, – 4

II. y2 + 10y + 25 = 0

or (y + 5)2 = 0

or y + 5 = 0

y = – 5

x > y

D.6-10): In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between x and y

6) I. 2x2 + x – 1 = 0

II) 2y2 + 13y + 15 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(a)

2x2 + 2x – x – 1 = 0

or 2x(x + 1) – 1(x + 1) = 0

or (2x – 1) (x + 1) = 0

∴x= -1,1/2

II. 2y2 + 3y + 10y + 15 = 0

or y(2y + 3) + 5(2y + 3) = 0

or (y + 5) (2y + 3) = 0 ∴y= -5, -3/2

x > y

7) I. x2 + 12x + 32 = 0

II) 2y2 + 15y + 27 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(e)

x2 + 4x + 8x + 32 = 0

or x(x + 4) + 8(x + 4) = 0

or (x + 4) (x + 8) = 0

x = – 4, – 8

II. 2y2 + 6y + 9y + 27 = 0

or 2y(y + 3) + 9(y + 3) = 0

or (2y + 9) (y + 3) = 0

∴y= -9/2, -3

No relation can be established between x and y.

8) I. 6x2 – 17x + 12 = 0

II) 7y2 – 13y + 6 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(a)

6x2 – 9x – 8x + 12 = 0

or 3x(2x – 3) – 4(2x – 3) = 0

or (2x – 3) (3x – 4) = 0

∴x=3/2,4/3

II. 7y2 – 7y – 6y + 6 = 0

or 7y(y – 1) – 6(y – 1) = 0

or (7y – 6) (y – 1) = 0

∴y=1,6/7

x > y

No relation between ‘x’ and ‘y’.

9) I. x2 – 82x + 781 = 0

II) y2 = 5041

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(e)

x2 – 11x – 71x + 781 =0

or x(x – 11) – 71(x – 11) = 0

or(x – 11)(x – 71) = 0

x = 11, 71

II. y2 = 5041

y = ± 71

10) I. 6x2 – 47x + 80 = 0

II) 2y2 – 9y + 10 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or no relation can be established between ‘x’ and ‘y’.

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(b)

6x2 – 15x – 32x + 80 = 0

or 3x (2x – 5) – 16(2x – 5) = 0

or (3x – 16) (2x – 5) = 0

∴x=16/3,  5/2

II. 2y2 – 4y – 5y + 10 = 0

or 2y(y – 2) – 5(y – 2) = 0

or (y – 2) (2y – 5) = 0

∴y=2,5/2