Quadratic Equations | Solved Problems and Practice Questions

Quadratic Equations | Solved Problems and Practice Questions

Online banking classes – Quadratic equations are one of the most important topics for banking as well as insurance exams as 5 questions are expected from this topic. In these types of questions, you will be given two quadratic equations roots of which you have to find & compare the values of the roots. 

Directions (1-10) : In each of the following questions two equations are given followed by 5 options. You have to solve the equations and give an answer:

 Quadratic Equations Questions

Q.1 I.  5x² + 29x + 20 = 0 
      II. 25y² + 25y + 6 = 0 
(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

 

 

Q.2 I.  3x² – 16x + 21 = 0
       II.  3y² – 28y + 65 = 0 
(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

3 I.  x² + x – 12 = 0 
   II. y² + 2y – 8 = 0

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

4 I. 4x² – 13x + 9 = 0 
   II. 3y² – 14y + 16 = 0  

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

5 I. 16x² + 20x + 6 = 0 
   II. 10y² + 38y + 24 = 0  

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

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Q. 6 I. 17x² + 48x = 9
        II. 13y² = 32y – 12

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

7 I. 8x² + 26x + 15 = 0 
   II. 4y² + 24y + 35 = 0 

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

8 I. 6x² + 19x + 15 = 0 
   II. 24y² + 11y + 1 = 0 

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

9 I. 2x² + 11x + 15 = 0  
   II.  4y² + 22y + 24 = 0 

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

 

10 I.  2x² + 9x + 9 = 0 
     II. 2y² + 17y + 36 = 0 

(a) if x < y
(b) if x ≤ y
(c) the relationship between x and y cannot be determined
(d) if x ≥ y
(e) if x > y

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Quadratic Equations Solutions

Solution 1.   Ans. (a)
Sol.
I. 5x² + 29 + 20 = 0
⇒ 5x² + 25x + 4x + 20 = 0
⇒ (x + 5) (5x + 4) = 0
⇒ x = –5, –4/5

1. 25y² + 25y + 6 = 0
   ⇒ 25y² + 15y + 10y + 6 = 0
   ⇒ (5y + 3) (5y + 2) = 0
   ⇒ y = – 3/5, –2/5
   y > x

 

Solution 2.  Ans. (a)
Sol.
I. 3x² – 16x + 21 = 0
⇒ 3x² – 9x – 7x + 21 = 0
⇒ (x – 3) (3x – 7) = 0
⇒ x = 3, 7/3

II. 3y² – 28y + 65 = 0
⇒ 3y² – 15y – 13y + 65 = 0
⇒ (y – 5)(3y – 13) = 0
⇒ y = 5, 13/3

y > x

 

Solution 3. Ans. (c)
Sol.
I. x² + x – 12 = 0
⇒ x² + 4x – 3x – 12 = 0
⇒ (x + 4) (x – 3) = 0
⇒ x = 3, –4

II. y² + 2y – 8 = 0
⇒ y² + 4y – 2y – 8 = 0
⇒ (y + 4) (y – 2) = 0
⇒ y = – 4, 2
No relation

Solution 4.  Ans. (c)
Sol.
I. 4x² – 13x + 9 = 0
⇒ 4x² – 4x – 9x + 9 = 0
⇒ (x – 1) (4x – 9) = 0
⇒ x = 1, 9/4

II. 3y² – 14y + 16 = 0
⇒ 3y² – 6y – 8y + 16 = 0
⇒ (y – 2) (3y – 8) = 0
⇒ y = 2, 8/3
No relation

 

Solutions 5. Ans. (e)
Sol.
I. 16x² + 20x + 6 = 0
⇒ 8x² + 10x + 3 = 0
⇒ 8x² + 4x + 6x + 3 = 0
⇒ (2x + 1) (4x + 3) = 0
⇒ x = –1/2, –3/4

 

1. 10y² + 38y + 24 = 0

⇒ 5y² + 19y + 12 = 0

⇒ 5y² + 15y + 4y + 12 = 0

⇒ (y + 3) (5y + 4) = 0

y = –3, –4/5

x > y

 

Solution 6. Ans. (a)
Sol.
I. 17x² + 48x – 9 = 0
⇒ 17x² + 51x – 3x – 9 = 0
⇒ (x + 3) (17x – 3) = 0
⇒ x = 3/17, – 3

II. 13y² – 32y + 12 = 0
⇒ 13y² – 26y – 6y + 12 = 0
⇒ (y – 2) (13y – 6) = 0
⇒ y = 2, 6/13
y > x

Solution 7. Ans. (d)
Sol.
I. 8x² + 26x + 15 = 0
⇒ 8x² + 20x + 6x + 15 = 0
⇒ 4x (2x + 5) + 3(2x + 5) = 0
⇒ (2x + 5) (4x + 3) = 0
⇒ x = – 5/2, –3/4

II. 4y² + 24y + 35 = 0
⇒ 4y² + 10y + 14y + 35 = 0
⇒ 2y (2y + 5) + 7 (2y + 5) = 0
⇒ (2y + 5) (2y + 7) = 0
⇒ y = –5/2, –7/2
x ≥ y

Solution 8. Ans. (a)
Sol.
I. 6x² + 19x + 15 = 0
⇒ 6x² + 9x + 10x + 15 = 0
⇒ (2x + 3) (3x + 5) = 0
⇒ x = –3/2, –5/3

II. 24y² + 11y + 1 = 0
⇒ 24y² + 8y + 3y + 1= 0
⇒ (3y + 1) (8y + 1) = 0
⇒ y = –1/3, –1/8
y > x

Solution 9. Ans. (c)
Sol.
I. 2x² + 11x + 15 = 0
⇒ 2x² + 6x + 5x + 15 = 0
⇒ (x + 3) (2x + 5) = 0
⇒ x = – 3, –5/2

II. 4y² + 22y + 24 = 0
⇒ 2y² + 11y + 12 = 0
⇒ 2y² + 8y + 3y + 12 = 0
⇒ (y + 4) (2y + 3) = 0
⇒ y = –4, –3/2
No relation

 

Solution 10. Ans. (e)
Sol.
I. 2x² + 9x + 9 = 0
⇒ 2x² + 6x + 3x + 9 = 0
⇒ (x + 3) (2x + 3) = 0
⇒ x = –3, –3/2

II. 2y² + 17y + 36 = 0
⇒ 2y² + 8y + 9y + 36 = 0
⇒ (y + 4) (2y + 9) = 0
y = – 4, –9/2
x > y

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