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If the polynomial x^2+bx+c has exactly one real root and b=c+1, find the value of the product of all possible values of c.

 Sep 5, 2018
 #1
avatar+67 
+1

never mind i found the answer its 1 btw

 Sep 5, 2018
 #2
avatar+100516 
+1

x^2+bx +c   ...  b  = c + 1  ....so....

 

x^2 + (c + 1)x + c

 

If this has one real root, the discriminant  = 0

 

So

 

(c + 1)^2  - 4(1)(c)  = 0  simplify

 

c^2 + 2c + 1  - 4c   = 0

 

c^2 - 2c + 1  = 0    this factors as

 

(c - 1)^2  = 0      take the square root

 

c - 1  = 0    ⇒   c  =  1

 

 

cool cool cool

 Sep 6, 2018

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