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The equation has equal roots. Find .

Class 10Quadratic EquationsAlgebra — Quadratics
  • A1
  • B−2
  • C4
  • D2

Step-by-Step Solution

Expand before touching the discriminant: . Now . The terms cancel, so gives the LINEAR equation → — which is why this one has a single answer rather than a pair. Check: gives . Answer −2 mis-signs the − term; 4 solves as read off the wrong side; 1 comes from cancelling the 4s carelessly to get .
Answer: D) 2

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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