Question

If (x +2k) is a factor of f(x) =x^5 -4k^2x^3 +3x +2k+3 , find k.

Answer 1

Answer:

k = 3/4

Step-by-step explanation:

ATQ,

f(x) = x^5 - 4k^2x^3 + 3x + 2k + 3

(x + 2k) is a factor

=> (-2k) is a zero

=> f(-2k) = 0

=> (-2k)^5 - 4k^2(-2k)^3 + 3(-2k) + 2k + 3 = 0

=> (-2k)^5 - (-2k)^2(-2k)^3 + 3(-2k) + 2k + 3 = 0

=> (-2k)^5 - (-2k)^5 + 3(-2k) + 2k + 3 = 0

=> 3(-2k) + 2k + 3 = 0

=> -6k + 2k = -3

=> -4k = -3

=> k = 3/4

Hope it helps :)

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