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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.

ANotSmartPerson  Oct 5, 2018
 #1
avatar+89874 
+3

If the polynomial  has one real root, the discriminant [ b^2 - 4ac ] must  = 0

 

So   a  =1, b  = c+ 1 ...so we have

 

(c + 1)^2  - 4(1)c    simplify

 

c^2 + 2c + 1  - 4c  = 0

 

c^2 - 2c + 1  = 0      factor the left side

 

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

 

c - 1  = 0

 

c  = 1

 

 

 

cool cool cool

CPhill  Oct 5, 2018
 #2
avatar+34 
+1

Thank you, that was fast!

ANotSmartPerson  Oct 5, 2018
edited by ANotSmartPerson  Oct 5, 2018

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