Question

Find the value of K if x+k is a factor of x raise to 4 minus k square x square plus three x minus 6k.

Answer 1

Solution:

Let p(x) = x⁴-k²x²+3x-6k

It is given that (x+k) is a factor of p(x).

Therefore,

p(-k) = 0

=> (-k)⁴-k²(-k)²+3(-k)-6k = 0

=> k⁴-k⁴-3k-6k = 0

=> -9k = 0

=> k = 0

Therefore,

k = 0

••••

Answer 2

Answer:

k=0

Step-by-step explanation:

Let p(x) = x⁴-k²x²+3x-6k

Given:

(x+k) is a factor of p(x).

So,

p(-k)=0

→ (-k)⁴-k²(-k)²+3(-k)-6k=0

→ k⁴-k⁴-3k-6k=0

→ -9k=0

→ k=0