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Arun applies the quadratic formula to . What does he find?

Class 10Quadratic EquationsAlgebra — Quadratics
  • A, so is not a real number and the equation has no real roots
  • B, so the roots are
  • C, so the roots are
  • D, so there is one repeated root

Step-by-Step Solution

. A negative discriminant means has no real value, so the formula produces no real roots and Arun should stop there. Reading as +23 flips the sign of the negative result — the single most common discriminant error. comes from 9 + 32, i.e. adding instead of subtracting it. would require , which is false here.
Answer: A) , so is not a real number and the equation has no real roots

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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