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The equation has real roots. What is the largest value can take?

Class 10Quadratic EquationsAlgebra — Quadratics
  • A1
  • B4
  • C−1
  • D2

Step-by-Step Solution

"Real roots" allows equal roots too, so the condition is D ≥ 0: ≥ 0 → ≤ 1. The largest permitted value is , where and the roots are equal. Answer 4 uses alone and ignores the factor; −1 reads the inequality backwards; 2 uses the coefficient of . Note that if the question had said "distinct" real roots, would have been excluded.
Answer: A) 1

Key idea: The discriminant — nature of roots

classifies the roots of **: TWO distinct real roots. Parabola crosses -axis at two points.
- ****: ONE repeated real root (called a 'double root' or 'two equal roots'). Parabola touches -axis at the vertex.
- ****: NO real roots. Parabola does not touch the -axis at all.

**Use case**: 'For what values of does have equal roots?' → set → .

You can answer 'how many real roots?' WITHOUT computing them — just compute .

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