Question

The value of k for which x+k is a factor of x³ +kx² -2x+k + 4 is (a) 2 (b) -5 (c) -4/5 (d) 6/7​

Answer 1

Answer:

The answer is $k=-\frac{4}{3}$

Step-by-step explanation:

Factor theorem: $x-a$ is a factor of polynomial $P(x)$ if $P(a)=0$

Here given $x+k=x-(k)$ is a factor of $P(x)=x^2+kx^2-2x+k+4$

        $\Rightarrow P(-k)=0\\\Rightarrow (-k)^3+k(-k)^2-2(-k)+k+4=0\\\Rightarrow -k^3+k^3+2k+k+4=0\\\Rightarrow 3k+4=0\\\Rightarrow 3k=-4\\\Rightarrow k=-\frac{4}{3}$