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

k=2

Step-by-step 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

Step-by-step 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

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

step-by-step explanation: