for what value of b in the equation (2z+b)(z-3)=0 will a solution for z be -4?

Question

For what value of b in the equation (2z+b)(z-3)=0 will a solution for z be -4?

Answer 1

(2z+b)(z-3)=0

 

According to the Zero Factor Property, the above equation will be true if (2z+b) = 0 and/or (z-3) = 0.  So, we want:

 

     2z + b = 0 when z = -4

 

     2(-4) + b = 0

 

     -8 + b = 0

 

Solve for b to get the answer.

Answer 2

We set z=-4

 

(2*-4 + b)(-4 - 3) = 0

 

(-8 + b)(-7) = 0

 

 

Set the factor (-8 + b) equal to 0.

 

-8 + b = 0

 

 

Solving for b, we get 8.

 

b = 8

 

 

Now we check this solution to be certain.  We plug in this value of b into the original equation. Then we solve for z.  We should get z=-4 as a solution.

 

(2z + 8)(z - 3) = 0

 

 

Set the factors equal to zero.

 

2z + 8 = 0          and            z - 3 = 0

 

 

Solve for both equations.

 

2z = -8                             z = 3

 

  z = -4

 

It checks out!