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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. 

 Dec 24, 2018
edited by Guest  Dec 24, 2018
edited by Guest  Dec 24, 2018
 #1
avatar+100473 
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We have that  

 

x^2 + (c + 1)x + c  = 0

 

If this has one real root, it is a double-root and the discriminant  = 0      

 

So.......

 

(c + 1)^2  - 4(1)c  = 0

 

c^2 + 2c + 1 - 4c  =  0

 

c^2 - 2c + 1  =  0      factor

 

(c - 1)^2  = 0

 

So.....c  = 1

 

This is the only value of c that makes this true....

 

cool cool cool

 Dec 24, 2018

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