Find the roots of 2x² − 9x + 4 = 0 with the quadratic formula.

Find the roots of $2 x^{2} - 9 x + 4 = 0$ with the quadratic formula.

Class 10Quadratic EquationsAlgebra — Quadratics

D = (- 9)^{2} - 4 (2) (4) = 81 - 32 = 49

, and

49 = 7

, so

x = \frac{9 \pm 7}{4}

, giving

x = 4

x = \frac{1}{2}

. Check

x = 4

: 32 − 36 + 4 = 0. The first option reports

- b /2 a

alongside one root. Making both roots negative contradicts the positive sum 9/2. "2 and

\frac{1}{4}

" has the right product

(\frac{1}{2})

but the sum is

\frac{9}{4}

, not

\frac{9}{2}

Answer: B) 4 and

\frac{1}{2}

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.