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ne of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root? \begin{align*} &-x^2 + 18x + 81 \\ &3x^2 - 6x + 9 \\ &8x^2 - 32x + 32 \\ &25x^2 - 30x - 9 \\ &x^2 - 14x + 196 \end{align*}

 Apr 23, 2022
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The repeated root   is the one  whose  discriminant  = 0

 

You can  check the others.....but the repeated root comes from

 

8x^2  - 32x + 32  because

 

32^2  - 4 (8) (32)  =

 

32^2  - 32^2   = 0

 

The repeated root  is      (32/8)  /2  =  4 /2  = 2

 

 

cool cool cool

 Apr 23, 2022
edited by CPhill  Apr 23, 2022

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