Which of these values is a root of 2x² − 7x − 4 = 0?

Which of these values is a root of $2 x^{2} - 7 x - 4 = 0$ ?

Class 10Quadratic EquationsAlgebra — Quadratics

Substitute

x = 4 : 2 (16) - 7 (4) - 4 = 32 - 28 - 4 = 0

, so 4 is a root. Factorising confirms it:

2 x^{2} - 7 x - 4 = (x - 4) (2 x + 1)

, so the roots are 4 and

- \frac{1}{2}

. Choosing

x = - 4

flips the sign of the wrong root; choosing

x = \frac{1}{2}

drops the minus sign from

- \frac{1}{2}

; choosing

x = \frac{7}{4}

uses

- b /2 a

, which is the midpoint of the two roots, not a root itself.

Answer: A)

x = 4

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.