Mathematics
Find the value of a, if x - 2 is a factor of 2x5 - 6x4 - 2ax3 + 6ax2 + 4ax + 8.
Factorisation
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Answer
x - 2 = 0 ⇒ x = 2.
Since, x - 2 is a factor of 2x5 - 6x4 - 2ax3 + 6ax2 + 4ax + 8,
∴ On substituting x = 2 in 2x5 - 6x4 - 2ax3 + 6ax2 + 4ax + 8, remainder = 0.
⇒ 2(2)5 - 6(2)4 - 2a(2)3 + 6a(2)2 + 4a(2) + 8 = 0
⇒ 2(32) - 6(16) - 2a(8) + 6a(4) + 8a + 8 = 0
⇒ 64 - 96 - 16a + 24a + 8a + 8 = 0
⇒ 16a - 24 = 0
⇒ 16a = 24
⇒ a = = 1.5
Hence, a = 1.5
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