Question

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.

Answer 1

Answer:

Step-by-step explanation:

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