Discussion

Explanation:

Given, 2x² – 3x – 2 = 0

Here, we need to find two numbers such that their sum = coefficient of x i.e., -3 and their product = (coefficient of x²) × (contant term) = 2 × - 2 = - 4.

The two such numbers are -4 and 1. 

Now, splitting the middle term, we get

⇒ 2x² – 4x + x – 2 = 0

⇒ 2x(x – 2) + (x – 2) = 0

⇒ (x - 2)(2x + 1) = 0

Either (x - 2) = 0 or (2x + 1) = 0

∴ x = 2 or -1/2.

Hence, option (a).

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