Which of the following is a quadratic equation?

Class 10Quadratic EquationsAlgebra — Quadratics

Step-by-Step Solution

A quadratic equation has the form

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

with a ≠ 0. Only

2 x^{2} - 3 x + 1 = 0

fits this degree-2 form.

Answer: B)

2 x^{2} - 3 x + 1 = 0

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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