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in Quadratic Equations by (46.2k points)
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Which of the following is a quadratic equation ?

(a) \(x^\frac12 + 2x +3 = 0\)

(b) (x - 1)(x + 4) = x2 + 1

(c) x4 - 3x + 5 = 0

(d) (2x + 1)(3x - 4) = 2x2 + 3

1 Answer

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Best answer

(d) (2x + 1)(3x - 4) = 2x2 + 3 

We reduce each of the given parts to standard form:

(a) \(x^\frac12 + 2x +3 = 0\) ⇒ degree = 1 ⇒ Not a quad. eqn.

(b) (x - 1)(x + 4) = x2 + 1 

⇒ x2 + 3x - 4  = x2 + 1 ⇒ 3x - 5 = 0 ⇒  Degree = 0 ⇒ Not a quad. eqn.

(c) x4 - 3x + 5 = 0 ⇒ Degree = 4 ⇒ Not a quad. eqn

(d) (2x + 1)(3x - 4) = 2x2 + 3 

⇒ 6x2 - 5x - 4 = 2x2 + 3 

⇒ 4x2 - 5x -4 = 0 ⇒ Degree = 2 ⇒ Hence a quad. eqn.

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