For what value of ‘a’, the polynomial 2x3 + ax2 + 11x

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For what value of ‘a’, the polynomial 2x³ + ax² + 11x + a + 3, is exactly divisible by (2x – 1) ?

Let, P(x) = 2x³ + ax² + 11x + a + 3
(2x – 1) is its factor.

∴ p		1		= 0
		2

⇒ 2 ×		1		³	+ a ×		1		²	+ 11 ×	1	+ a + 3 = 0
		2					2				2

⇒	1	+	a	+	11	+ a + 3 = 0
	4		4		2

⇒	1 + a + 22 + 4a + 12	= 0
	4

⇒	5a + 35	= 0
	4

⇒ 5a + 35 = 0 ⇒ 5a = – 35
⇒ a = –7