Question

if x+2k is a factor of p(x)=x^5-4k^2x^3+2x+2k+3,
find k

Answer 1

Answer :

Given polynomial is

p(x) = x^5 - 4k²x³ + 2x + 2k + 3

Since, (x + 2k) is a factor of p(x), x = - 2k will satisfy the polynomial valuing to 0.

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

⇒ -32k^5 + 32k^5 - 4k + 3 = 0

⇒ -4k + 3 = 0

⇒ 4k = 3

⇒ k = 3/4

∴ k = 3/4

#MarkAsBrainliest

Answer 2

Answer:

k=3/2

Step-by-step explanation:

x+2k is a factor of

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

x+2k=0

x= (-2k)

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

(-2*-2*-2*-2*-2)k - 4k^2 * (-2*-2*-2)k + (-4k) + 2k + 3= 0

-32k^5 - 4k^2 * (-8k^3) + [(-4k) + 2k] + 3 = 0

-32k^5 + 32k^5 - 2k + 3 = 0

-2k + 3= 0

-2k= (-3)

k= -3/-2 [ negative / negative = positive]

Final answer:

k= 3/2