Quadratic Equation For IBPS RRB Exam, Important Question with Solution

The IBPS RRB exam is a highly competitive exam that tests candidates on various subjects, including quantitative aptitude. One of the crucial topics in this section is quadratic equations. Understanding and mastering quadratic equations can significantly enhance a candidate’s performance in the quantitative aptitude section. This article provides a detailed overview of quadratic equations, essential concepts, and a set of important questions with detailed solutions to help you prepare effectively for the IBPS RRB exam.

What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial equation in a single variable x, with the highest power of x being 2. It is generally represented in the standard form as:

ax² + bx + c = 0

where a, b and c are constants, a is not equal to 0. The solutions to the quadratic equation are known as the roots of the equation.

Key Concepts

Standard Form & Roots

• The quadratic equation ax² + bx + c = 0 has two roots, which can be found using the quadratic formula.
• The term b² − 4ac is called the discriminant (D), and it determines the nature of the roots.
  • If D>0, the equation has two distinct real roots.
  • If D=0, the equation has two equal real roots.
  • If D<0, the equation has two complex roots.

Factoring Method:

• For some quadratic equations, factoring can be a simpler method to find the roots. The equation ax² + bx + c = 0 can sometimes be factored into the form (dx + e) (fx + g) = 0, where the roots can be found by setting each factor equal to zero.

Completing the Square

• Another method to solve quadratic equations is by completing the square. This involves transforming the equation into the form (x−p)² = q and then solving for x.

Quadratic Equation For IBPS RRB Exam

Directions (1-5): In each of these questions, two equations (i) and (ii) are given. You have to solve both the equations and give answer

(a) if x>y

(b) if x≥y

(c) if x = y or no relation can be established between x and y.

(d) if y>x

(e) if y≥ 𝑥

Q1. (i) x² – 12x + 32 = 0

(ii) y² – 20y + 96 = 0

Q2. (i) 2x² – 3x – 20 = 0

(ii) 2y² + 11y + 15 = 0

Q3. (i) x² – x – 6 = 0

(ii) y² – 6y + 8 = 0

Q4. (i) x² + 14x – 32 = 0

(ii) y² – y – 12 = 0

Q5. (i) x² – 9x + 20 = 0

(ii) 2y² – 12y + 18 = 0

Directions (6-10): There are two equations (I) and (II) in x and y are given in each question. You have to solve both the equations and give answer accordingly:

(a) if x > y

(b) if x < y

(c) if x = y or relation between x & y cannot be established

(d) x ≥ y

(e) x ≤ y

Q6. I. 6x² + x – 2 = 0

II. 10y² – 23y – 5 = 0

Q7. I. 12x² – 12x = 13x – 12

II. 12y² – 13y + 3 = 0

Q8. I. x² + 14x – 32 = 0

II. y² – y – 12 = 0

Q9. I. x² – 9x + 20 = 0

II. 2y² – 12y + 18 = 0

Q10. I. 𝑥 − 5 = − 6/x

II. 𝑦 − 4 = − 4/𝑦

Directions (11-15): In each question two equations numbered (I) and (II) are given. You have to solve both the equations and mark appropriate answer.

(a) If 𝑥 < 𝑦

(b) If 𝑥 > 𝑦

(c) If 𝑥 ≥ 𝑦

(d) If 𝑥 ≤ 𝑦

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

Q11. I. 2x² – 17x + 36 = 0

II. 3y² – 22y + 40 = 0

Q12. I. x² + 21x + 108 = 0

II. y² + 14y + 48 = 0

Q13. I. 2x² + 7x – 60 = 0

II. 3y² – 28y + 64 = 0

Q14. I. x² – 2x – 24 = 0

II. y² + 3y – 40 = 0

Q15. I. 𝑥³ = 729

II. 𝑦² − 15𝑦 + 54 = 0

Directions (16-20): Two equations I and II are given below in each question. You have to solve these equations and give answer accordingly.

(a) if x<y

(b) if x>y

(c) if x≤y

(d) if x≥y

(e) if x=y or no relation can be established

Q16. I. 3𝑥² + 17𝑥 + 10 = 0

II.10𝑦² + 9𝑦 + 2 = 0

Q17. I. 4𝑥² = 49

II. 9𝑦² − 66𝑦 + 121 = 0

Q18. I. 3𝑥² + 5𝑥 + 2 = 0

II. 𝑦² + 12𝑦 + 27 = 0

Q19. I. 𝑥² − 7𝑥 + 10 = 0

II. 𝑦² − 14𝑦 + 45 = 0

Q20. I. 6𝑥² − 49𝑥 + 99 = 0

II. 5𝑦² + 17𝑦 + 14 = 0

Directions (21-25): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.

(a) if x>y

(b) if x≥y

(c) if x<y

(d) if x ≤y

(e) if x = y or no relation can be established between x and y.

Q21. (I) 8x²–10x+3=0

(II) 5y²+14y–3=0

Q22. (I) 3x²+13x+12=0

(II) y²+9y+20=0

Q23. (I) x²–4x–5=0

(II)7y²–25y–12=0

Q24. (I) x³=216

(II)2y²–25y+78=0

Q25. (I) 5x² + 31x + 48 = 0

(II) 3y² + 27y + 42 = 0

Directions (26-30): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x>y

(b) if x≥y

(c) if x<y

(d) if x ≤y

(e) if x = y or no relation can be established between x and y

Q26. I. (𝑥 − 2)² − 4 = 0

II. 𝑦² + 1 − 2𝑦 = 0

Q27. I. 3𝑥 + 2𝑦 = 5

II. 4𝑥 + 6𝑦 = 10

Q28. I. 9𝑥² – 54𝑥 + 77 = 0

II. 12y² – 55y + 63 = 0

Q29. I. (𝑥 – 1) ² = 121

II. y² – 24y + 144 = 0

Q30.I. 7𝑥² – 23𝑥 + 6 = 0

II. y² – 7y + 12 = 0

Directions (31-35): In each of these questions, two equations (I) and (II) are given. Solve the equations and mark the correct option:

(a) if x>y

(b) if x≥y

(c) if x<y

(d) if x ≤y

(e) if x = y or no relation can be established between x and y.

Q31. I. x² + x – 12 = 0

II. y² – 9y + 14 = 0

Q32. I. 6x² + 5x + 1 = 0

II. 4y² – 15y = 4

Q33. I. 3x² + x − 2 = 0

II. 12y² + 7y + 1 = 0

Q34. I. 𝑥‑² + 13𝑥 + 42 = 0

II. 𝑦² + 8𝑦 + 12 = 0

Directions (36-40): In each of these questions, two equation (I) and (II) are given. You have to solve both the equations and give answer

(a) If x>y

(b) If x≥y

(c) If x<y

(d) If x≤y

(e) If x = y or no relation can be established between x and y

Q36. I. 2x² – 31x + 84 = 0

II. 3y² + y – 2 = 0

Q37. I. x² – 30x + 216 = 0

II. y² – 21y + 108 = 0

Q38. I. x² – 8x + 15 = 0

II. y² – 11y + 30 = 0

Q39. I. 3𝑥² − 13𝑥 + 14 = 0

II. 2𝑦² − 17𝑦 + 33 = 0

Q40. I. x² + 11x + 28 = 0

II. y² – 22y + 105 = 0

Solution
1	2	3	4	5	6	7	8	9	10
e	b	c	c	a	c	d	c	a	d
11	12	13	14	15	16	17	18	19	20
c	a	d	e	c	a	a	b	c	b
21	22	23	24	25	26	27	28	29	30
a	a	e	d	e	e	e	b	d	d
31	32	33	34	35	36	37	38	39	40
e	c	e	d	e	a	b	d	c	c

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