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Which value of satisfies BOTH and ?

Class 10Quadratic EquationsAlgebra — Quadratics
  • A
  • B
  • C
  • DThere is no common value

Step-by-Step Solution

gives or −3. gives or 1. The only value in both lists is −3. Check: 9 − 9 = 0 and 9 − 6 − 3 = 0. Picking 3 uses only the first equation, picking 1 uses only the second, and "no common value" is what you get if you solve with the signs reversed.
Answer: B)

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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