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Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.
\(\begin{align*} &-x^2 + 18x + 81 \\ &3x^2 - 3x - 168 \\ &x^2 - 4x - 4 \\ &25x^2 - 30x + 9 \\ &x^2 - 14x + 24 \end{align*}\)

 May 12, 2020
 #1
avatar+111326 
+2

We can  only  have  a repeated  root  whenever  the discriminant  =  0

 

First one   18^2 - 4(-1)(81)  > 0    so no repeated root

 

Second one     (-3)^2  - 4(3) (-168)  >  0    so no repeated root

 

Third one   (-4) - (4) (1) (-4)  > 0      so no repeated root

 

Fourth one  (-30)^2  - 4(25) (9)   =  900 - 100(9)  =  0      repeated root

Note  this factors  as  (5x - 3)^2

(5x - 3)^2  = 0     take both roots

5x - 3  = 0

5x  = 3

x  =  3/5   = repeated root

 

 

cool cool cool

 May 12, 2020
 #2
avatar+133 
+2

Thank You So Much!!!

 May 12, 2020

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