In quadratic equation questions, two equations with 2 different variables are given. You have to find out the values of the variables and compare them and find the relation between them. Similarly, in some questions information is given in two statements named as Quantity 1 and Quantity 2. You have to study the information along with the question and compare the values derived from Quantity 1 and Quantity 2 then select the answer accordingly. In SBI PO or Clerk exam, a minimum of 5 questions will come from these models.
Directions(Q.1-5): In the following questions, two equations are given. You have to solve both and establish the relation between given variables.
1. I. x2 - 11x + 28 = 0
II. y2 - 18y + 81 = 0 (SBI Clerk 2018)
Ans: x < y
Explanation: I. x2 - 11x + 28 = 0
By solving the equation,
x = 7 and 4
II. y2 - 18y + 81 = 0
By solving the equation,
y = 9 and 9
∴ x < y
2. I. 2x2 + 9x + 7 = 0
II. y2 + 4y + 4 = 0
Ans: x = y or the relationship cannot be established
Explanation:
I. 2x2 + 9x + 7 = 0
⇒ 2x2 + 7x + 2x + 7 = 0
⇒ (2x + 7)(x +1) = 0
⇒ 7 x = -1 or - 
II. y2 + 4y + 4 = 0
⇒ y2 + 2y + 2y + 4 = 0
⇒ y(y + 2) + 2(y + 2) = 0
⇒ y = -2, -2
∴ relationship can't be established
3. I. 3x2 - 14x + 16 = 0
II. 5y2 - 16y + 12 = 0 (SBI Clerk 2018)
Ans: x ≥ y
Explanation:
I. 3x2 - 14x + 16 = 0
⇒ 3x2 - 6x - 8x + 16 = 0
⇒ 3x(x - 2) - 8(x - 2) = 0
x = 2, 
II. 5y2 - 16y + 12 = 0
⇒ 5y2 - 10y - 6y + 12 = 0
⇒ 5y(y - 2) - 6(y - 2) = 0
⇒ 6 y = 2, ¾ \ x ≥ y
4. I. x2 - 8x + 15 = 0
II. y2 - 12y + 36 = 0
Ans: x < y
Explanation:
I. x2 - 8x + 15 = 0
⇒ x2 - 5x - 3x + 15 = 0
⇒ (x - 3)(x - 5) = 0
⇒ x = 3 or 5
II. y2 - 12y + 36 = 0
⇒ y2 - 6y - 6y + 36 = 0
⇒ y(y - 6) - 6(y - 6) = 0
⇒ y = 6, 6
∴ x < y
5. I. x2 - 9x + 20 = 0
II. y2 = 16
Ans: x ≥ y
Explanation:
I. x2 - 9x + 20 = 0
⇒ x2 - 5x - 4x + 20 = 0
⇒ (x - 5) (x - 4) = 0
⇒ x = 4 or 5
II. y2 = 16
⇒ y = 
⇒ y = 4 or -4
∴ x ≥ y
Directions (Q.6 - 10): In each of the questions below, two equations are provided. On the basis of these you have to find out the relation between p and q.
Give answer 1) if p = q or no relation
Give answer 2) if p > q
Give answer 3) if p < q
Give answer 4) if p ≥ q
Give answer 5) if p ≤ q
6. 2p2 + 19p + 42 = 0;
4q2 + 43q + 30 = 0 (SBI Clerk 2018)
Ans: 1
Explanation:
2p2 + 19p + 42 = 0
⇒ 2p2 + 12p + 7p + 42 = 0
⇒ 2p(p + 6) + 7(p + 6) = 0
⇒ 7 p = - 6, - 
4q2 + 43q + 30 = 0
⇒ 4q2 + 40q + 3q + 30 = 0
⇒ 4q(q + 10) + 3(q + 10) = 0
⇒ 3 q = -10, - ¾
∴ There is No relation
7. q2 + q = 2 ; p2 + 7p + 10 = 0
Ans: 5
Explanation:
q2 + q = 2
by solving we get q values as 1 and -2
p2 + 7p + 10 = 0
by solving we get p values as -2 and -5
∴ p ≤ q
8. 3p2 + 23p + 30 = 0; 6q2 + 13q + 5 = 0 (SBI Clerk 2016)
Ans: 5
Explanation:
3p2 + 23p + 30 = 0
⇒ 3p2 + 18p + 5p + 30 = 0
⇒ 3p(p + 6) +5(p + 6) = 0
⇒ 5 p = - 6, - 
6q2 + 13q + 5 = 0
⇒ 6qv + 3q + 10q + 5 = 0
⇒ 3q(2q + 1) + 5(2q + 1) = 0
∴ p ≤ q
9. p2 + 36 = 12p ; 4q2 + 144 = 48q
Ans: 1
Explanation:
p2 + 36 = 12p
by solving we get p values as 6 and 6;
4q2 + 144 = 48q
by solving we get q values as 6 and 6
∴ p = q
10. 2p2 + 12p + 16 = 0
2q2 + 14q + 24 = 0
Ans: 4
Explanation:
2p2 + 12p + 16 = 0
by solving we get p values as -4 and -2;
2q2 + 14q + 24 = 0
by solving we get q values as -3 and -4
∴ p ≥ q
