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Find all real numbers $z$ for which the equation $(z-5)x^2-zx+5=0$ only has one real solution. If you find more than one, then list the values separated by commas.

 Jan 26, 2019
 #1
avatar+104069 
0

(z-5)x^2-zx+5=0   

 

Again....if this only has one real root......the discriminant = 0 

 

z^2 -  4(z - 5)(5)  = 0

 

z^2 -  20(z - 5) = 0

 

z^2 - 20z + 100 = 0

 

(z  -  10) (z -10) = 0

 

(z - 10)^2 = 0

 

z - 10 = 0

 

z = 10

 

 

cool cool cool

 Jan 26, 2019
 #2
avatar+23 
+1

I got this problem wrong on the homework.

 Jan 27, 2019

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