Quadratic Equations Question for SBI PO, Clerk and IBPS Exam

Quadratic Equations Question for SBI PO, Clerk and IBPS Exam

Quadratic Equations Question for SBI PO, Clerk and IBPS Exam

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

Q.1 

I. 35x2 – 11x – 6 = 0               II. 5y2 – 23y + 12 = 0

(A) if x < y

(B) if x > y

(C) if x ≤ y

(D) if x ≥ y

(E) if x = y or relationship between x and y can’t be established

 

Q.2

I. x2 × 2161/3 = √576 x 22                II. y3 – √1225 = √841

(A) if x < y

(B) if x > y

(C) if x ≤ y

(D) if x ≥ y

(E) if x = y or relationship between x and y can’t be established

 

Q.3 

I. 72x2 + 59x + 12 = 0               II. 44y2 + 67y + 15 = 0

(A) if x < y

(B) if x > y

(C) if x ≤ y

(D) if x ≥ y

(E) if x = y or relationship between x and y can’t be established

 

Q.4

I. (
x
 4
 – 2) (
x
 3
 – 5) = 0
II. √ × y2 =
49 × 3431/3
      √7         .

(A) if x < y

(B) if x > y

(C) if x ≤ y

(D) if x ≥ y

(E) if x = y or relationship between x and y can’t be established

 

Q.5

I. √484 x (1331)1/3 x X = 5082

II.
 √ y 
 21
 +
 √ y 
  7
 = √ 16

(A) if x < y

(B) if x > y

(C) if x ≤ y

(D) if x ≥ y

(E) if x = y or relationship between x and y can’t be established

 

Answer 1. (C) if x ≤ y

Explanation:

I. 35x2 – 11x – 6 = 0

35x2 – 21x + 10x – 6 = 0

7x (5x – 3) + 2 (5x – 3) = 0

(5x – 3) (7x + 2) = 0

x = 3/5, –2/7

 

II. 5y2 – 23y + 12 = 0

5y2 – 20y – 3y + 12 = 0

5y (y – 4) – 3 (y – 4) = 0

(y – 4) (5y – 3) = 0

y = 4, 3/5

 

Answer 2. (C) if x ≤ y

Explanation:

I. x2 × 2161/3 = √576 x 22

x2 × 6 = 24 x 4

x2 = 16

x = ± 4

 

II. y3 – √1225 = √841

y3 – 35 = 29

y3 = 29 + 35

y3 = 64

y = 4

 

Answer 3. (E) if x = y or relationship between x and y can’t be established

Explanation:

I. 72x2 + 59x + 12 = 0

72x2 + 27x + 32x + 12 = 0

9x (8x + 3) + 4 (8x + 3) = 0

(8x + 3) (9x + 4) = 0

x = – 3/8, – 4/9

 

II. 44y2 + 67y + 15 = 0

44y2 + 55y + 12y + 15 = 0

11y (4y + 5) + 3 (4y + 5) = 0

(11y + 3) (4y + 5) = 0

y = – 3/11, – 5/4

 

Answer 4. (B) if x > y

Explanation:

I. (
x
 4
 – 2) (
x
 3
 – 5) = 0
I. (
x -8
  4
) (
x – 15
   3
) = 0

(x – 8) (x – 15) = 0

x = 8, 15

II. √ × y2 =
49 × 3431/3
      √7         .
II. y1/2 × y2 =
72 × 7
   71/2  .

y5/2 = 72 + 1 – 1/2

y5/2 = 75/2

y = 7

 

Answer 5. (A) if x < y

Explanation:

I. √484 x 13311/3 x X= 5082

22 x 11 x X = 5082

x = 21

II.
 √ y 
 21
 +
 √ y 
  7
 = √ 16
 y  + 3√ y 
      2    
 = 4

4√ y  = 84

 y  = 21

y = 441

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