Question

The value of K for which x+K is a factor of x³ + Kx²- 2x + K+4 is



Options are
1 )
$2$

2)
$- 5$

3)
$\frac{ - 4}{3}$

4)
$\frac{6}{7}$

​

Answer 1

Answer:

Correct option is

A

−

3

4

Let f(x)=x

3

+kx

2

−2x+k+4

If x+k is a factor of f(x) then-

f(−k)=0

f(−k)=(−k)

3

+k(−k)

2

−2(−k)+k+4

−k

3

+k

3

+2k+k+4=0

Hence,

k=

3

−4

This is the required value of k.

Answer 2

Convert given polynomial into equation as:

x^3 +kx^2 -2x +k + 4 = 0 …..(A)

Since x+k is a factor,substitute x= -k in (A), you will get, - k^3 +k^3 + 2k +k +4 = 0

Ultimately you will get, k = -4/3

the correct ans for ur QUESTION is option c -4/3

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