Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. - Mathematics

Find the value of a, if x – 2 is a factor of 2x⁵ – 6x⁴ – 2ax³ + 6ax² + 4ax + 8.

Sum

f(x) = 2x⁵ – 6x⁴ – 2ax³ + 6ax² + 4ax + 8

x – 2 = 0 `\implies` x = 2

Since, x – 2 is a factor of f(x), remainder = 0.

2(2)⁵ – 6(2)⁴ – 2a(2)³ + 6a(2)² + 4a(2) + 8 = 0

64 – 96 – 16a + 24a + 8a + 8 = 0

–24 + 16a = 0

16a = 24

a = 1.5

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