ICSE Class 10 Mathematics: Quadratic Equations — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: Solve: x² - 7x + 12 = 0 by factorisation.
  Ans: x² - 7x + 12 = 0. Find two numbers whose product = 12 and sum = -7: -3 and -4. x² - 3x - 4x + 12 = 0. x(x - 3) - 4(x - 3) = 0. (x - 3)(x - 4) = 0. x = 3 or x = 4.
• Q: Solve using the quadratic formula: 2x² + 5x - 3 = 0.
  Ans: Using x = (-b ± √(b²-4ac)) / 2a. a=2, b=5, c=-3. D = b²-4ac = 25+24 = 49. √D = 7. x = (-5 ± 7)/4. x = (-5+7)/4 = 1/2 or x = (-5-7)/4 = -3. Solutions: x = 0.5 or x = -3.
• Q: The sum of a number and its reciprocal is 10/3. Find the number.
  Ans: Let number = x. x + 1/x = 10/3. (x² + 1)/x = 10/3. 3x² + 3 = 10x. 3x² - 10x + 3 = 0. 3x² - 9x - x + 3 = 0. 3x(x-3) - 1(x-3) = 0. (3x-1)(x-3) = 0. x = 1/3 or x = 3.

Long Answer / Application Questions (4-6 Marks)

• Q: Find the nature of roots of 3x² - 5x + 2 = 0 without solving.
  Ans: Discriminant D = b² - 4ac = (-5)² - 4(3)(2) = 25 - 24 = 1. Since D > 0 and is a perfect square, the roots are real, unequal, and rational.

Exam Tips for This Chapter

• Revise all definitions and laws from Quadratic Equations — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Quadratic Equations — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Quadratic Equations carries 8-12 marks in the board exam