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Showing 1 question in Mathematics for Class 10. Tap a card to reveal the answer.
MathematicsQuadratic EquationsmediumFind 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.