Quadratic Equation Quiz Set -2 IBPS PO | IBPS RRB| IBPS Clerk| SBI| RBI

Quadratic Equation Quiz

Quadratic Equation Quiz. Welcome to Online Quantitative Aptitude Section in  letsstudytogether.co .Quadratic Equation is one of the most favourite topics of almost every banking exam. Here we are providing a Quiz Set on Quadratic Equation so that you can practice more and get good marks in the examination.

Quadratic Equation Quiz Set -2

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Directions: In each of these questions two equations numbered I and II are given. You have to solve both the equations and give answer.

1. I. 9x2-6x-35=0

    II. 3y2-y-10=0

(a) if x < y

(b) if x ≤ y

(c) if x = y or Relationship between x and y cannot be established

(d) if x > y

(e) if x ≥ y

Show Correct Answers

C. if x = y or Relationship between x and y cannot be established

From I,
9x2 + 15x – 21x – 35 = 0
3x(3x + 5)-7(3x + 5) = 0
(3x – 7)(3x + 5) = 0
x = 7/3 or -5/3
From II,
3y2– y – 10 = 0
3y2– 6y + 5y – 10 = 0
3y(y – 2)+5(y – 2) = 0
y = -5/3 or 2
So, no relationship can be established between
x and y.

2. I. 85x2-77x-30=0
    II. 255y2– 231y-90=0

(a) if x < y

(b) if x ≤ y

(c) if x = y or Relationship between x and y cannot be established

(d) if x > y

(e) if x ≥ y

Show Correct Answers

C. if x = y or Relationship between x and y cannot be established

From I,
85x2– 77x – 30 = 0
85x2– 102x + 25x – 30 = 0
17x(5x – 6) + 5(5x – 6) = 0
(17x + 5)(5x – 6) = 0
x = -5/17 or 6/5
From II,
255y2– 231y – 90 = 0
3(85y2– 77y – 30) = 0
85y2– 77y – 30 = 0
y = -5/17 or 6/5
So, no relationship can be established between
x and y.

3. I. 7x2– 45x + 50 = 0
    II. 21y2– 44y + 20 = 0

(a) if x < y

(b) if x ≤ y

(c) if x = y or Relationship between x and y cannot be established

(d) if x > y

(e) if x ≥ y

Show Correct Answers

E. if x ≥ y

From I,
7x2– 45x + 50 = 0
7x2– 35x – 10x + 50 = 0
7x(x – 5)-10(x – 5) = 0
(7x – 10)(x – 5) = 0
x = 10/7 or 5
From II,

21y2– 44y + 20 =0

21y2– 14y – 30y + 20 = 0
7y(3y – 2)-10(3y – 2) = 0
(7y – 10)(3y – 2) = 0
y = 10/7 or 2/3
So, x ≥ y.

4. I. 12x2-24x+12=0
II. 5y2-7y – 6=0

(a) if x < y

(b) if x ≤ y

(c) if x = y or Relationship between x and y cannot be established

(d) if x > y

(e) if x ≥ y

Show Correct Answers

C. if x = y or Relationship between x and y cannot be established

From I,
12x2-12x – 12x + 12 = 0
12x(x – 1)-12(x – 1) = 0
(12x – 12)(x – 1) = 0
x = 1
From II,
5y2– 7y – 6 = 0
5y2– 10y – 3y – 6 = 0
5y(y – 2)-3(y – 2) = 0
y = 2/5 or 2
So, no relationship can be established between x and y.

 5. I. 2x2-3x+1=0
     II. 15y2-16y + 4=0

(a) if x < y

(b) if x ≤ y

(c) if x = y or Relationship between x and y cannot be established

(d) if x > y

(e) if x ≥ y

Show Correct Answers

C. if x = y or Relationship between x and y cannot be established

From I,
2x2– 3x + 1 = 0
2x2– 2x – x + 1 = 0
2x(x – 1) – 1(x – 1) = 0
(2x – 1)(x – 1) = 0
x = 1/2 or 1

From II,
15y2– 16y + 4 = 0
15y2-10y – 6y + 4 = 0
5y(3y – 2)-3(3y – 2) = 0
(5y – 3)(3y – 2) = 0
y = 3/5 or 2/3
So, no relationship can be established between
x and y.

6. I. x2 +4x -5 = 0
II. y2-20y +19 = 0

(a) x < y

(b) x > y

(c) x ≤ y

(d) x ≥ y

(e) x = y or relationship cannot be established

Show Correct Answers

C. x ≤ y

From equation I:
x2 +4x -5 = (x -1)(x + 5)= 0
=> x = 1, -5
From equation II:
y2-20y +19 = (y -1)(y -19) = 0
=> y = 1, 19

 X =1 X = -5
Y = 1  x = y  x < y
Y = 19  x < y  x < y

So, x ≤ y

7. I. x2 +17x +52 = 0
    II. 6y2 +y -40 = 0

(a) x < y

(b) x > y

(c) x ≤ y

(d) x ≥ y

(e) x = y or relationship cannot be established

Show Correct Answers

A. x < y

From equation I:
x2 +17x +52 = (x + 4)(x + 13)= 0
=> x = -4, -13
From equation II:
6y2 +y -40 = (3y + 8)(2y -5) = 0
=> y = -8/3, 5/2

 X= -4  X = -13
Y=-8/3   x < y  x < y
Y = 5/2  x < y  x < y

So, x < y

8. I. x2 + 12 = 7x
II. y2 + 30 = 11y

a) x > y
b) x ≥ y
c) x < y
d) x ≤ y
e) x = y or the relationship cannot be established

Show Correct Answers

C. x < y

From I,
x2– 7x + 12 = 0
=> x=3,4
From II,
y2– 11y + 30 = 0
=> y=5,6
Hence x<y

9. I.  x2– 5x – 14 = 0
II. 3y2 + 17y + 22 = 0

a) If x ≤ y

b) If x ≥ y

c) If x < y

d) If x > y

e) If x = y or no specific relation can be established.

Show Correct Answers

B. If x ≥ y

First equation –
x2– 5x – 14 = 0
or, x2– 7x + 2x – 14 = 0
or, x (x – 7) + 2 (x – 7) = 0
or, (x – 7) (x + 2) = 0
or, x = – 2 or 7
Second equation –
3y2 + 17y + 22 = 0
or, 3y2 + 11y + 6y + 22 = 0
or, y (3y + 11) + 2 (3y + 11) = 0
or, (y + 2) (3y + 11) = 0
or, y = – 2 or – 11/3
So here x is always more than y or equals to y so the answer is 2

10. I. 12x2– 25x + 12 = 0
II. 2y2– 7y + 6 = 0

a) If x ≤ y

b) If x ≥ y

c) If x < y

d) If x > y

e) If x = y or no specific relation can be established.

Show Correct Answers

C. If x < y

First equation –
12x2– 25x + 12 = 0
or, 12x2– 16x – 9x + 12 = 0
or, 4x (3x – 4) – 3 (3x – 4) = 0
or, (4x – 3) (3x – 4) = 0
or, x = ¾ or 4/3
Second equation –
2y2– 7y + 6 = 0
or, 2y2– 4y – 3y + 6 = 0
or, 2y (y – 2) – 3 (y – 2) = 0
or, (2y – 3) (y – 2) = 0
or, y = 3/2 or 2
So here we can see that y is always more than x. The answer is 3.


Quadratic Equation Quiz Set -1 

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