Answer:
Every value of b>4.47 and b<-4.47 will cause the quadratic equation
to have two real number solution.
Step-by-step explanation:
We have the quadratic function
, and we have to find the value of b.
A <em>quadratic function</em> is
, a quadratic function usually has two real solutions. You can find that solutions using Bhaskara's Formula:


and
are real solutions of the quadratic equation if and only if:

If
the quadratic equation doesn't have real solutions.
If
the quadratic equation has only one solution.
Then in this case to have two real number solutions: 
We have
, where a=1, b, c=5
Then,

Adding 20 in both sides of the equation:

Which is the same as: 
Then, 
Then every value of b>4.47 and b<-4.47 will cause the quadratic equation
to have two real number solution.
For example b=-5 or b=5.
If you replace with b=-5 in 

Then the quadratic function has two real number solutions.