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For Class 8, 9 & 10

Foundation - a strong base in Physics, Chemistry, Maths & Biology

Concept-first questions with clear model answers across all four subjects, aligned to NCERT. Start early, build the habit, and walk into your board exams, NEET and JEE already ahead.

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Showing 1 question for Class 10. Tap a card to reveal the answer.

MathematicsQuadratic Equationsmedium

Find the roots of x^2 - 5x + 6 = 0 and state the nature of the roots using the discriminant.

Reveal answer ↓

What it is

The discriminant D = b^2 - 4ac reveals the nature of a quadratic's roots before you solve it.

Answer

Factorise: (x - 2)(x - 3) = 0, so the roots are x = 2 and x = 3. The discriminant D = b^2 - 4ac = (-5)^2 - 4(1)(6) = 25 - 24 = 1. Since D > 0 and is a perfect square, the roots are real, distinct and rational.

D = b^2 - 4ac ; x = (-b +/- sqrt(D)) / 2a

  • •(x-2)(x-3) = 0 -> roots 2, 3
  • •D = b^2 - 4ac = 1
  • •D > 0 -> two distinct real roots

Why learn this

Engineers use it to know at a glance if a design has real solutions (bridges, projectiles).

💡 Memory trick

D > 0 real and distinct; D = 0 real and equal; D < 0 no real roots.