Question

If x +2k is a factor of p(x)=x4 -4k2 x2+2x+3k+3 find k

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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[] 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]
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$<marquee>Thank you and Happy Diwali.</marquee>$

Answer 2

X+2k=0
x=-2k substitute in p(x)
p(-2k)=(-2k)^4-4k^2×(-2k)^2+2(-2k)+3k+3
=16k^4-16k^4-4k+3k+3
=-k+3
if p(-2k)=0 then
-k+3=0
k=3