Use the quadratic formula on 2x² + x − 4 = 0.

Use the quadratic formula on $2 x^{2} + x - 4 = 0$ .

Class 10Quadratic EquationsAlgebra — Quadratics

a = 2, b = 1, c = - 4. D = b^{2} - 4 a c = 1 - 4 (2) (- 4) = 1 + 32 = 33

, and

2 a = 4

, so

x = \frac{- 1 \pm 33}{4}

. The first option forgets the minus sign in front of

b . 31

comes from computing 1 − 32 instead of 1 + 32 — the classic sign slip when

c

is negative. The last option divides by a instead of

2 a

Answer: C)

\frac{- 1 \pm 33}{4}

The general solution to

a x^{2} + b x + c = 0

(any quadratic):

**

x

= [−

b

± √

(b^{2} - 4 a c)

] /

(2 a) * *

Derivation: complete the square on

a x^{2} + b x + c = 0

in full generality.

**Always works** when

D = b^{2} - 4 a c

≥ 0. When

D < 0

, no real roots exist (complex roots only — Class 11 territory).

**Example**:

3 x^{2} - 5 x + 2 = 0. a = 3, b = - 5, c = 2. D = 25 - 24 = 1. x

= (5 ± 1) / 6 →

x = 1

or 2/3.

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