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.
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.
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.
Read The Hindu Editorial Vocabulary to know difficult words with its meanings. We provide monthly…
Punjab & Sind Bank LBO Phase II Result 2025 is out. Download the PDF to…
Decode the RBI's December 2025 Repo Rate cut. Learn what the 'Goldilocks' economy means and…
Download SSC CPO Admit Card 2025 for SI in Delhi Police & CAPFs. Check exam…
Click on the Blog to check IBPS RRB Clerk Prelims 2025 all shifts section‑wise analysis,…
Click here to download free PDF of Static GK Questions for RRB NTPC. Boost your…