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Find the difference between the roots of x^2 - 7x - 9 = 0.

 May 19, 2020
 #1
avatar+675 
+2

answer=sqrt85

Feel free to ask how I got this answer, and tell me if this is correct or not:)

 May 19, 2020
 #2
avatar+1498 
+4

Just to expalin

 

The quadratic formula is

 

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

 

So we have

 

\(x = {7 \pm \sqrt{-7^2-4*(-9)} \over 2} = {7 \pm \sqrt{49-36} \over 2} = {7 \pm \sqrt{13} \over 2}\)

 

That's then +/- sqrt(13), so the difference is (7+sqrt(13))/2 - (7-sqrt(13))/2 =

 

(7 - 7 + sqrt(13) - ( - sqrt(13))/2 = 2(sqrt(13))/2 = sqrt(13)

 

So I believe the answer is sqrt(13)

 

So I don't understand where the sqrt(85) came from.

 May 19, 2020
 #3
avatar+675 
+2

thanks, hugo for explaining, I really appreciate it:)

 May 19, 2020

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