We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
175
4
avatar+151 

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.

 Jan 6, 2019

Best Answer 

 #2
avatar+701 
+1

If the polynomial has 1 real root, then the discriminant mut equal 0. We can rewrite the polynomial as \(x^2 + cx + x + c\).

 

The discriminant is always \(b^2-4ac\), and setting a = 1 and b = c+1, we have \((c+1)^2 - 4c = 0\). Simplifying, we have \(c^2 + 2c +1 - 4c = 0 \Rightarrow c^2 - 2c +1 = 0\). Factoring, we have \((c-1)^2 = 0\). Taking the square root of both sides, we have \(c -1 = 0 \Rightarrow \boxed{c = 1}\).

 

There is only one solution since there is only once real root. The product of all possible values of c is 1. 

 

Hope this helps,

- PM

 #1
avatar+5225 
+3

\(\text{1 real root indicates that the Discriminate }D = b^2 - 4ac \text{ is equal to }0\\ D=(c+1)^2 - 4(1)(c) = \\ c^2 + 2c + 1 - 4c =\\ c^2 - 2c+1 = 0\)

 

\((c-1)^2 = 0\\ c=1\)

.
 Jan 6, 2019
edited by Rom  Jan 6, 2019
 #3
avatar+701 
+4

I am pretty sure you factored \(c^2 - 2c + 1 = 0\) incorrectly. 

 #2
avatar+701 
+1
Best Answer

If the polynomial has 1 real root, then the discriminant mut equal 0. We can rewrite the polynomial as \(x^2 + cx + x + c\).

 

The discriminant is always \(b^2-4ac\), and setting a = 1 and b = c+1, we have \((c+1)^2 - 4c = 0\). Simplifying, we have \(c^2 + 2c +1 - 4c = 0 \Rightarrow c^2 - 2c +1 = 0\). Factoring, we have \((c-1)^2 = 0\). Taking the square root of both sides, we have \(c -1 = 0 \Rightarrow \boxed{c = 1}\).

 

There is only one solution since there is only once real root. The product of all possible values of c is 1. 

 

Hope this helps,

- PM

 #4
avatar+101804 
+2

Good job, PM...!!!!

 

cool cool cool

CPhill  Jan 6, 2019

18 Online Users

avatar