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avatar+1791 

One of the five quadratics below has a repeated root.  (The other four have distinct roots.)  What is the repeated root?
-x^2 - 18x + 49
3x^2 - 6x + 48
8x^2 - 32x + 16
25x^2 - 30x + 9
x^2 - 14x + 16

 Nov 7, 2023
 #1
avatar+36919 
+1

Repeated root is 3/5  ( or 0.6) 

 

By completing the square: 

25 x^2 -30x + 9 =0 

25 ( x^2 -1.2x)    + 9 = 0 

25 (x - .6)^2     - 9   + 9   = 0 

25 ( x -.6)^2 = 0    shows two roots at x = 0.6   ( or  3/5) 

 Nov 9, 2023

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