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Quadratic Equations – Free Practice Questions

Quadratic Equations is part of Maths (Quantitative Aptitude) in government exams such as SSC MTS, SSC CHSL, SSC CGL, RRB Group D / Level-1, RRB NTPC and others. This page has 200 free practice questions in English and Hindi, with correct answers and explanations and short revision notes.

द्विघात समीकरण – हिंदी और अंग्रेज़ी में 200 निःशुल्क अभ्यास प्रश्न, उत्तर और व्याख्या के साथ।

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Questions: 200 · Sets of 50: 4 · Difficulty mix: 200 medium · Languages: English and Hindi

Sample Quadratic Equations questions with answers

Q1. What are the roots of x² − 5x + 6 = 0?

x² − 5x + 6 = 0 के मूल क्या हैं?

  1. 1 and 6
  2. 2 and 3
  3. −2 and −3
  4. −1 and 6
Answer: 2 and 3. x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3.
x² − 5x + 6 = (x − 2)(x − 3) = 0, अतः x = 2 या x = 3

Q2. Find the roots of x² − 9x + 20 = 0

x² − 9x + 20 = 0 के मूल ज्ञात करें।

  1. 4 and 5
  2. 4 and −5
  3. 5 and 6
  4. −5 and −4
Answer: 4 and 5. Find two numbers with sum 9 and product 20: 4 and 5.
ऐसी दो संख्याएँ जिनका योग 9 और गुणनफल 20 हो: 4 और 5

Q3. Find the roots of x² + 10x + 9 = 0

x² + 10x + 9 = 0 के मूल ज्ञात करें।

  1. −8 and 0
  2. 1 and 9
  3. −9 and 1
  4. −9 and −1
Answer: −9 and −1. Find two numbers with sum −10 and product 9: −9 and −1.
ऐसी दो संख्याएँ जिनका योग −10 और गुणनफल 9 हो: −9 और −1

Q4. If one root of x² − 9x + c = 0 is 3, find c.

यदि x² − 9x + c = 0 का एक मूल 3 है, तो c ज्ञात करें।

  1. 6
  2. 27
  3. 21
  4. 18
Answer: 18. The other root = 9 − 3 = 6. c = product of roots = 3 × 6 = 18.
दूसरा मूल = 9 − 3 = 6। c = मूलों का गुणनफल = 3 × 6 = 18

Q5. If one root of x² − 12x + c = 0 is 3, find c.

यदि x² − 12x + c = 0 का एक मूल 3 है, तो c ज्ञात करें।

  1. 27
  2. 9
  3. 30
  4. 36
Answer: 27. The other root = 12 − 3 = 9. c = product of roots = 3 × 9 = 27.
दूसरा मूल = 12 − 3 = 9। c = मूलों का गुणनफल = 3 × 9 = 27

Q6. Find the roots of x² + 6x − 27 = 0

x² + 6x − 27 = 0 के मूल ज्ञात करें।

  1. −8 and 4
  2. −3 and 9
  3. −9 and −3
  4. −9 and 3
Answer: −9 and 3. Find two numbers with sum −6 and product −27: −9 and 3.
ऐसी दो संख्याएँ जिनका योग −6 और गुणनफल −27 हो: −9 और 3

Q7. If one root of x² − 13x + c = 0 is 7, find c.

यदि x² − 13x + c = 0 का एक मूल 7 है, तो c ज्ञात करें।

  1. 42
  2. 6
  3. 91
  4. 49
Answer: 42. The other root = 13 − 7 = 6. c = product of roots = 7 × 6 = 42.
दूसरा मूल = 13 − 7 = 6। c = मूलों का गुणनफल = 7 × 6 = 42

Q8. If one root of x² − 11x + c = 0 is 2, find c.

यदि x² − 11x + c = 0 का एक मूल 2 है, तो c ज्ञात करें।

  1. 9
  2. 18
  3. 22
  4. 20
Answer: 18. The other root = 11 − 2 = 9. c = product of roots = 2 × 9 = 18.
दूसरा मूल = 11 − 2 = 9। c = मूलों का गुणनफल = 2 × 9 = 18

Q9. What is the product of the roots of 4x² − 18x − 11 = 0?

4x² − 18x − 11 = 0 के मूलों का गुणनफल क्या है?

  1. 9/2
  2. 11/4
  3. 15/4
  4. −11/4
Answer: −11/4. For ax² + bx + c = 0, sum of roots = −b/a and product = c/a. Here the product = −11/4.
ax² + bx + c = 0 में मूलों का योग = −b/a और गुणनफल = c/a। यहाँ गुणनफल = −11/4।

Q10. What is the product of the roots of 5x² + 10x + 17 = 0?

5x² + 10x + 17 = 0 के मूलों का गुणनफल क्या है?

  1. −17/5
  2. 22/5
  3. 17/5
  4. −2
Answer: 17/5. For ax² + bx + c = 0, sum of roots = −b/a and product = c/a. Here the product = 17/5.
ax² + bx + c = 0 में मूलों का योग = −b/a और गुणनफल = c/a। यहाँ गुणनफल = 17/5।
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