<u>Answer-</u>

<u>Solution-</u>
Rational Root Theorem-

All the potential rational roots are,

The given polynomial is,

Here,

The potential rational roots are,


From, the given options only  satisfies.
 satisfies.
 
        
                    
             
        
        
        
Step-by-step explanation:
k² + 5k + 13 = 0
Using the quadratic formula which is

From the question
a = 1 , b = 5 , c = 13
So we have

<u>Separate the solutions</u>

The equation has complex roots 
<u>Separate the real and imaginary parts</u>
We have the final answer as

Hope this helps you
 
        
             
        
        
        
Answer:
3
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
5/6. Is this what u are looking for?
Step-by-step explanation:
Step 1 Simplify:2x(6)-19=-9 to 12x+-19=-9
Step 2 Add 19 to both sides: 12x-19+19=-9+19. You should get 12x=20
Step 3 Divide 12 on both sides: 12x/12=10/12
x=10/12. Simplified= x=5/6
 
        
             
        
        
        
We start with 

 and wish to write it as 

First, pull 2 out from the first two terms: 

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have 

 and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square: 

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have 

 and when we multiply that out it does not give us what we started with. It gives us 

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.
We do this as follows: 

 which gives us the final expression we seek:

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e =  -103
We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106