If (x – a) is the HCF of x² + x – 12 and 2x² – ax – 9, then the value of 'a' is :यदि x² + x – 12 और 2x² – ax – 9 का म०स०प० (x – a) हो, तो 'a' का मान है :

1. A3
2. B–3
3. C–4
4. D4

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Correct answer: A. 3

Explanation

x² + x − 12 = (x + 4)(x − 3), so the HCF is either (x + 4) or (x − 3). If a = 3, then 2x² − 3x − 9 = (2x + 3)(x − 3), which has (x − 3) as a factor. If a = −4, then 2x² + 4x − 9 is not divisible by (x + 4). Hence a = 3.x² + x − 12 = (x + 4)(x − 3), अतः म०स०प० (x + 4) या (x − 3) होगा। a = 3 लेने पर 2x² − 3x − 9 = (2x + 3)(x − 3), जिसका एक गुणनखंड (x − 3) है। a = −4 लेने पर 2x² + 4x − 9 , (x + 4) से विभाज्य नहीं है। अतः a = 3।