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in Polynomials by (24.0k points)
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If (x + 1) is a factor of x4 + 9x3 + 7x2 + 9ax + 5a2, then :

(a) a = 137 

(b) 5a2 – 9a – 1 = 0

(c) 5a2 + 9a + 17 = 0 

(d) a = \(\sqrt{131}\)

1 Answer

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Best answer

(b) 5a2 – 9a – 1 = 0

Let f (x) = x4 + 9x3 + 7x2 + 9ax + 5a2

If (x + 1) is a factor of f (x), then 

f(–1) = 0 ⇒ (–1)4 + 9 (–1)3 + 7 (–1)2 + 9a (–1) + 5a2 = 0 

⇒ 1 – 9 + 7 – 9a + 5a2 = 0 ⇒ 5a2 – 9a – 1 = 0.

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