If x-2 is a factor of x^5-2ax^3+a^2x-2 then sum of values of a is?

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If x-2 is a factor of x^5-2ax^3+a^2x-2 then sum of values of a is?

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Aubrey 1 month 2021-08-21T22:02:26+00:00 1 Answer 0 views 0

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    2021-08-21T22:04:25+00:00

    Answer:

    x-2 is a factor, so x = 2 is a root.

    so, 2^5 – 2a(2)³ + a²(2) – 2 = 0

    32 – 16a + 2a² – 2 = 0

    2a² – 16a + 30 = 0

    a² – 8a + 15 = 0

    a² – 5a – 3a + 15 = 0

    a(a-5)-3(a-5) = 0

    (a-5)(a-3) = 0

    either a = 5 or a = 3

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