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The quadratic x^2 + 5x + c = 0 has roots in the form of $x = \frac{-5 \pm \sqrt{17}}{2}$. What is the value of ?

 Jun 28, 2021
 #1
avatar+234 
+2

The quadratic formula is in format,

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

In this equation, \(x^2 + 5x + c = 0\), a = 1, and b = 5, as we are given that. The only term in the formula that contains c is the discriminant, \(\sqrt{b^2-4ac} = \sqrt{17}\)

Square both sides,

\(b^2-4ac = 17\)

Plug in known values,

\(25-4c = 17\)

Subtract 25 on both sides and divide by -4 to get c = 2

 Jun 28, 2021
 #2
avatar+120966 
+2

THX,  Awesomeguy    !!!!

 

Here's another  method

 

By Vieta, the product of the roots  =  c

 

So   c =  

 

(-5 + sqrt 17) /2   (  -5  -sqrt 17)  / 2   =

 

(25  - 17)  /  4   =

 

8 /  4   =  2

 

 

cool cool cool

 Jun 28, 2021

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