Question

If find the value of k, if x + k is a factor of the polynomial x 3 + kx 2 – 2x + k + 5.

Answer 1

Answer:

k = –5/3

Note:

★ If (x - a) is a factor of the given polynomial p(x) , then x = a is a zero of the polynomial p(x) and p(a) = 0 .

Solution:

Here,

The given polynomial is ;

x³ + kx² - 2x + k + 5

Let the given polynomial be p (x) .

Thus,

p(x) = x³ + kx² - 2x + k + 5

Also,

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

If x + k = 0

then x = -k

Thus,

=> p(-k) = 0

=> (-k)³ + k(-k)² - 2•(-k) + k + 5 = 0

=> -k³ + k³ + 2k + k + 5 = 0

=> 3k + 5 = 0

=> 3k = -5

=> k = -5/3

Hence,

The required value of k is (–5/3) .