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Suppose 2x^2 - 5x + k = 0 that  is a quadratic equation with one solution for x. Express k as a common fraction.

 

Also, pls include an explanation that is as clear as possible.

 

Thx

 Feb 18, 2019
 #1
avatar+104756 
+2

If we only have a single solution, then the discriminant = 0

 

So

 

(-5)^2 - 4(2)(k) = 0

 

25 - 8k  =  0

 

25 = 8k     

 

25 / 8 = k

 

The polynomial  is  2x^2 - 5x + 25/8

 

And the  single  root  (solution) to this is   x = 5/4

 

 

 

cool cool cool

 Feb 18, 2019
 #2
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+1

QS: according to my math book, it says that if the discriminent=0, it has a double root. sooo

Guest Feb 18, 2019
edited by Guest  Feb 18, 2019
 #3
avatar+104756 
+2

Eh......a slight mis-statement by me....we have a single root with a multiplicity of 2

 

So....we actually  have a "double root"....but....it's the same repeated root....

 

See the graph here :

 

 

 

cool cool cool

CPhill  Feb 18, 2019

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