Question

If 2x+1 is a factor of 2x³ +x²-kx-1, find the value of k​

Answer 1

Explanation:

2x+1=0

x=-1/2

Now p(x)= 2x^3 + x^2 -kx-1

subtitute value of x:

p(-1/2)= 2(-1/2)^3 + (-1/2)^2 -k(-1/2)-1

p(-1/2)=2*-1/8+1/4+k/2-1

p(-1/2)=-1/4+1/4+k/2-1

p(-1/2)=k/2-1

2x+1 is the factor of p(x) so

k/2-1=0

k/2=1

k= 2

Answer 2

k=2

Explanation:

Find the zeros of the factor

2x+1=0

x=-½

Plug x=-½ into the function and equate to 0

2(-½)³+(-½)²-k(-½)-1=0

2(-1/8)+¼+½k-1=0

-¼-1+¼+½k=0

-1+½k=0

½k=1

k=2