Quadratic Equation for SBI PO: The questions from the quadratic equation are more or less tricky and difficult in nature. But by practicing the right set of questions they are as easy as any other quant topic. We today have six questions, 3 each of prelims and mains with answer key.

Quadratic Equation for SBI PO Prelims Questions
1.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. (x + 4)2 = 23x – 20
II. (y – 3)2 = 3 – y
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: d)
Solution:
From I:
(x + 4)2 = 23x – 20
x2 + 8x + 16 = 23x – 20
x2 – 15x + 36 = 0
x2 – 3x – 12x + 36 = 0
x(x – 3) – 12(x – 3) = 0
(x – 3)(x – 12) = 0
x = 12, 3
From II:
(y – 3)2 = 3 – y
y2 – 6y + 9 = 3 – y
y2 – 5y + 6 = 0
y2 – 2y – 3y + 6 = 0
y(y – 2) – 3(y – 2) = 0
(y – 2)(y – 3) = 0
y = 2, 3
X | Relation | y |
12 | > | 2 |
12 | > | 3 |
3 | > | 2 |
3 | = | 3 |
So, x ≥ y
Hence, option d.

2.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. x2 = 324
II. y2 + 18y = 0
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: c)
Solution:
From I:
x2 = 324
x = -18, 18
From II:
y2 + 18y = 0
y(y + 18) = 0
y = 0, -18
X | Relation | y |
-18 | < | 0 |
-18 | = | -18 |
18 | > | 0 |
18 | > | -18 |
So, the relationship cannot be established.
Hence, option c.
3.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. x3 = -729
II. y2 + 15y + 54 = 0
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: e)
Solution:
From I:
x3 = -729
x = -9
From II:
y2 + 15y + 54 = 0
y2 + 6y + 9y + 54 = 0
y(y + 6) + 9(y + 6) = 0
(y + 9)(y + 6) = 0
y = -9, -6
X | Relation | y |
-9 | = | -9 |
-9 | < | -6 |
So, x ≤ y
Hence, option e.

Quadratic Equation for SBI PO Mains Questions
1.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. x + 19√x + 90 = 0
II. y + 23√y + 130 = 0
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: e)
Solution:
From I:
x + 19√x + 90 = 0
x + 9√x + 10√x + 90 = 0
√x(√x + 9) + 10(√x + 9) = 0
(√x + 10)(√x + 9) = 0
√x = -10, -9
x = 100, 81
From II:
y + 23√y + 130 = 0
y + 10√y + 13√y + 130 = 0
√y(√y + 10) + 13(√y + 10) = 0
(√y + 10)(√y + 13) = 0
√y = -10, -13
y = 100, 169
x | Relation | y |
100 | = | 100 |
100 | < | 169 |
81 | < | 100 |
81 | < | 169 |
So, x ≤ y
Hence, option e.
2.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. x2 + (9√3)x + 60 = 0
II. y2 + (6 + 4√3)y + 24√3 = 0
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: e)
Solution:
From I:
x2 + (9√3)x + 60 = 0
x2 + (5√3)x + (4√3)x + 60 = 0
x(x + 5√3) + 4√3(x + 5√3) = 0
(x + 5√3)(x + 4√3) = 0
x = -5√3, -4√3
From II:
y2 + (6 + 4√3)y + 24√3 = 0
y2 + 6y + (4√3)y + 24√3 = 0
y(y + 6) + 4√3(y + 6) = 0
(y + 4√3)(y + 6) = 0
y = -4√3, -6
x | Relation | y |
-5√3 | < | -4√3 |
-5√3 | < | -6 |
-4√3 | = | -4√3 |
-4√3 | < | -6 |
So, x ≤ y.
Hence, option e.

3.) In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y and choose the correct option.
I. 81x2+ 144x + 55 = 0
II. 81y2+ 180y + 91 = 0
a.) x > y
b.) x < y
c.) x = y or the relationship cannot be established
d.) x ≥ y
e.) x ≤ y
Answer: c)
Solution:
From I:
81x2+ 144x + 55 = 0
81x2+ 99x + 45x + 55 = 0
9x(9x + 11) + 5(9x + 11) = 0
(9x + 5)(9x + 11) = 0
x = -5/9, -11/9
From II:
81y2+ 180y + 91 = 0
81y2+ 117y + 63y + 91 = 0
9y(9y + 13) + 7(9y + 13) = 0
(9y + 7)(9y + 13) = 0
y = -7/9, -13/9
x | Relation | y |
-5/9 | > | -7/9 |
-5/9 | > | -13/9 |
-11/9 | < | -7/9 |
-11/9 | > | -13/9 |
So, the relationship cannot be established
Hence, option c.

Find daily exam updates posted on our official Instagram handle as well.
You might want to subscribe to our push notifications for such daily valuable articles.
Still, have some doubts about what we discussed in this blog? Then, leave your queries in the comment section below. We will surely respond to them.
- Sign Up on Practicemock for Updated Current Affairs, Free Topic Tests and Free Mini Mocks
- Sign Up Here to Download Free Study Material
Free Mock Tests for the Upcoming Exams
- IBPS PO Free Mock Test
- RBI Grade B Free Mock Test
- IBPS SO Free Mock Test
- NABARD Grade A Free Mock Test
- SSC CGL Free Mock Test
- IBPS Clerk Free Mock Test
- IBPS RRB PO Free Mock Test
- IBPS RRB Clerk Free Mock Test
- RRB NTPC Free Mock Test
- SSC MTS Free Mock Test
- SSC Strenographer Free Mock Test
- GATE Mechanical Free Mock Test
- GATE Civil Free Mock Test
- RRB ALP Free Mock Test
- SSC CPO Free Mock Test
- AFCAT Free Mock Test
- SEBI Grade A Free Mock Test
- IFSCA Grade A Free Mock Test
- RRB JE Free Mock Test
- Free Banking Live Test
- Free SSC Live Test