Question

If x + 2k is a factor of f(x) = x4

- 4k2x

2 + 2x + 3k + 3, find k?


step by step
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Answer 1

Answer:

Given, p(x) = x⁴ - 4k²x² + 2x + 3k + 3

And, x + 2k is a factor.

So, p(-2k) = 0

→→→ Putting -2k in place of x,

=> p(-2k) = (-2k)⁴ - (4 × k² × -2k²) + 2(-2k) + 3k + 3

=> 0 = 16k⁴ - 4k²(4k²) - 4k + 3k + 3

=> 0 = 16k⁴ - 16k⁴ - 4k + 3k + 3

=> 0 = -k + 3... [cancelling 16k⁴ and -16k⁴]

=> k = 3... [shifting k to LHS]