Chapter 4 — Lesson 3 ax² + bx + c = 0 Quadratic Equations Discriminant: b² − 4ac Nature of Roots
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Nature of Roots — Discriminant
📹 Video · 12 min CBSE Class 10 Chapter 4 · Unit 3
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📝 My Notes
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What you'll learn

  • Understand what the discriminant (D = b² − 4ac) tells us
  • Determine the nature of roots (real, equal, or imaginary)
  • Solve NCERT exercises on nature of roots
  • Apply the quadratic formula to real problems
  • Crack CBSE board exam questions on this topic

About this lesson

In this lesson, we explore the discriminant of a quadratic equation and how its value determines the nature of roots. This is a core CBSE Class 10 Maths topic from Chapter 4 (Quadratic Equations). You'll see animated step-by-step explanations, real NCERT examples, and solved board exam questions.

Prerequisites
✅ Factorization of polynomials
✅ Completing the square
✅ Quadratic formula basics
What's Next
📐 Word Problems on Quadratics
📐 Relationship between roots
📐 Quadratic Graphs

Standard Form

ax² + bx + c = 0

A quadratic equation where a ≠ 0 and a, b, c are real numbers.

Quadratic Formula

x = −b ± √(b²−4ac) / 2a

Always gives the roots. Use when factorization is not obvious.

Discriminant (D)

D = b² − 4ac

D > 0 → 2 real roots
D = 0 → equal roots
D < 0 → no real roots

Sum & Product of Roots

α+β = −b/a  |  αβ = c/a

α and β are the two roots. Useful for relationship-based questions.

🏆 CBSE Board Tip

In CBSE board exams, questions on discriminant are almost always 2–3 marks. Always state the value of D clearly and then conclude nature of roots in a separate line to get full marks.

Practice Question 1

Find the discriminant of 3x² − 5x + 2 = 0 and determine the nature of its roots.

🧠 Take Full Quiz on Quadratic Equations →
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Riya Sharma · 2 hours ago

Really helpful explanation! I always confused D=0 with D<0. The animation made it super clear. Thank you! 🙏

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Karan Mehta · 5 hours ago

Sir can you explain why when D<0 we say "no real roots" — do the roots still exist just as complex numbers?

Course Content
Class 10 — Mathematics
Progress48% · 7/15 chapters

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