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A student writes and starts hunting for the discriminant. What should she notice first?

Class 10Quadratic EquationsAlgebra — Quadratics
  • AIt is quadratic with a = 1, so D = 16 − 20
  • BIt is quadratic with a = 2
  • CIt has no solution at all
  • DThe terms cancel — it is really the linear equation

Step-by-Step Solution

Left side: . Right side: . Subtracting, → , i.e. . Since the terms cancel the equation is linear, so there is no discriminant to find. It is not quadratic with or (both assume the survives), and it certainly has a solution, .
Answer: D) The terms cancel — it is really the linear equation

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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