+0  
 
0
31
1
avatar

The quadratic equation 2x^2 + bx + 18 = x^2 + 6x + 4 has a double root.  Find all possible values of b.

 Apr 15, 2022
 #1
avatar+63 
+4

We can simplify first:

 

x^2 + (b - 6)x + 14 = 0

 

Now we can use a bit of brute force here:

 

(x + p)(x + q) 

 

pq = 14

p + q = b - 6

 

(p, q) = (14, 1) (7, 2) (-14, -1) (-7, -2)

 

So we can plug the values of p and q in to get all the possible values of b:

 

14 + 1 = b - 6 --> b = 21

7 + 2 = b - 6 --> b = 15

-14 + -1 = b - 6 --> b = -9

-7 + -2 = b - 6 --> b = -3

 

Thus, all the possible values of b are: 21, 15, -9, -3.

 

⚡⚡⚡

ShockFish

 Apr 15, 2022

14 Online Users