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The graph of just touches the -axis at one point (orange) to the right of the -axis. Find and the nature of the roots of .

Class 10Quadratic EquationsAlgebra — Quadratics
  • Ak = 6; two equal real roots
  • Bk = −6; two distinct real roots
  • Ck = −6; two equal real roots
  • Dk = −6; no real roots

Step-by-Step Solution

Touching the -axis once means : the roots are real and equal. The equal root is positive, so (then ).
Answer: C) k = −6; two equal 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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