Assertion (A): $x^{2} - 4 x + 4 = 0$ has two equal roots. Reason (R): A quadratic with discriminant zero has coincident roots. Which is correct?

Class 10Quadratic EquationsAlgebra — Quadratics

Step-by-Step Solution

For

x^{2} - 4 x + 4 = 0, D = 16 - 16 = 0

, giving the equal roots

x = 2

, 2. R states the general rule and correctly explains A.

Answer: A) Both A and R are true, and R is the correct explanation of A

D = b^{2} - 4 a c

classifies the roots of

a x^{2} + b x + c = 0 : - * * D > 0

**: TWO distinct real roots. Parabola crosses

x

-axis at two points.
- **

D = 0

**: ONE repeated real root (called a 'double root' or 'two equal roots'). Parabola touches

x

-axis at the vertex.
- **

D < 0

**: NO real roots. Parabola does not touch the

x

-axis at all.

**Use case**: 'For what values of

k

does

k x^{2} + 2 x + 1 = 0

have equal roots?' → set

D = 0 : 4 - 4 k = 0

→

k = 1

.

You can answer 'how many real roots?' WITHOUT computing them — just compute

D

Don't just memorise the answer — build a daily practice habit.