Assertion (A): The equation x² + 1 = 0 has no real roots. Reason (R): Its discriminant is negative. Which is correct?

Assertion (A): The equation $x^{2} + 1 = 0$ has no real roots. Reason (R): Its discriminant is negative. Which is correct?

Class 10Quadratic EquationsAlgebra — Quadratics

For

x^{2} + 1 = 0, D = 0 - 4 (1) (1) = - 4 < 0

, so there are no real roots. The negative discriminant is exactly the reason, so R 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.