Question

find the value of k if x+ 1 is a factor of p( x) in each of the following cases ( i ) p( x ) = x² + x + k​

Answer 1

Given:

• p(x) = x²+x+k
• factor of p(x) is x+1

To find:

• Value of k

Solution:

Here, given that x + 1 is factor of x² + x + k.

Now,

if x + 1 is factor of x² + x + k then x + 1 = 0

=> x + 1 = 0

=> x = -1

• From here, we found value of x = -1

So, if we put value of x in p(x) then it will be equal to 0

Therefore,

P(x) = x² + x + k

[ putting x = -1]

P(-1) = (-1)² + (-1) + k = 0

=> 1 -1 + k = 0

=> 0 + k = 0

=> k = 0

• Hence, the value of k will be 0

Answer 2

Solution -

Given equation,

• p(x) = x² + x + k

⠀

It is also given that (x + 1) is a factor of the given equation. If (x + 1) is a factor of p(x), then

• x + 1 = 0
• x = -1

⠀

Now, it is the factor of p(x), then x = -1 satisfy the given equation.

⠀

According to given condition

⇝ p(x) = x² + x + k

⇝ p(-1) = (-1)² + (-1) + k

⇝ p(-1) = 1 - 1 + k

⇝ p(-1) = k

⠀

Since, p(x) = 0

•°• p(-1) = k = 0

⠀

⠀⠀Thus, value of k is 0