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.
In this blog, we have provided the SSC CGL Syllabus 2025 and PDF for Tier…
Check SSC Calendar 2025 to know the notification and exam dates of SSC CGL, CHSL,…
In this blog, we have provided the DI for SSC CGL Exam. Practice free topic-wise…
In this blog, we have provided the 1200+ One Word Substitution for SSC CGL Exam…
Maximize your RBI Grade B prep with expert-recommended books. From Economics to Reasoning, find the…
RRB will release the RRB NTPC Exam Date 2025. Candidates can expect the Exam to…