QQuestion
The nature of the roots of the equation 3x² − 6x − 3 = 0 is:
(a) Real and equal
(b) Real, distinct and rational
(c) Real, distinct and irrational
(d) No real roots
ICSEClass 10MathematicsQuadratic Equations01 Mark2026 Moderate
✓Answer
(c) Real, distinct and irrational
Explanation:
For 3x² − 6x − 3 = 0:
a = 3, b = −6 and c = −3
Discriminant, D = b² − 4ac
⇒ D = (−6)² − 4 × 3 × (−3)
⇒ D = 36 + 36 = 72
Since D > 0, the roots are real and distinct. Since 72 is not a perfect square, the roots are irrational.
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