Question

Find the value of k ,if x+k is a factor of f(x)=x³+kx²-2x+k+5​

Answer 1

Answer:

If x+k is a factor, then the remainder when f(x) is divided by x+k is 0.

So, x+k = 0.

→ x = -k

Now substitute x = -k in f(x) = 0

You get,

-k³+k³+2k+k+5 = 0

→ k = -5/3

Conclusion:

So, k = -5/3

Answer 2

SOLUTION:-

⇒ x + k = 0

⇒ x = -k

Putting x = -k in f(x)

f(x) = x³ + kx² - 2x + 5

f(-k) = (-k)³ + k(-k)² - 2(-k) + k + 5

f(-k) =  -k³ + k³ + 2k + k + 5

f(-k) =  3k + 5

We know that,

f(-k) = 0

Hence,

⇒ 3k + 5 = 0

⇒ 2k = -5

⇒ k = $\frac{-5}{3}$

The value of x + k = x - $\frac{-5}{3}$

Hope it helps:)