+0  
 
-1
13
2
avatar+1066 

Find the constant $k$ such that the quadratic $2x^2 + 3x + 8x + k - x^2 + 20x$ has a double root.

 Jan 8, 2024
 #1
avatar+128732 
+1

2x^2 + 3x + 8x + k - x^2 + 20x    simplify

 

x^2 + 31x + k

 

To have a double root, the discriminant must  = 0

 

So

 

31^2 - 4 (1)k  = 0

 

961  - 4k  = 0

 

961  = 4k

 

k = 961 / 4

 

 

cool cool cool

 Jan 8, 2024
 #2
avatar+36919 
+1

Simplify to 

x^2 + 31x + k        now complete the square for 'x'

(x+ 15.5)^2    - 240.25   + k       will have a double root at x = -15.5   when  k = 240.25 

 Jan 8, 2024

1 Online Users