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For which positive integer values of k does \(kx^2+20x+k=0\) have rational solutions? Express your answers separated by commas and in increasing order.

 May 20, 2020
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For which positive integer values of k does kx² + 20x + k = 0  have rational solutions? Express your answers separated by commas and in increasing order.

 

Hello Guest!

 

 \(kx^2+20x+k=0 \)

 \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ a=c=k\\ b=20\\ x = {-20 \pm \sqrt{20^2-4k^2} \over 2k}\\ x = {-20 \pm \sqrt{400-4k^2} \over 2k}\)

 \(x = {-20 \pm 2\sqrt{100-k^2}\over2k}\)

\(k=\{1,2,3,4,5,6,7,8,9,10\}\)

laugh  !

 
 May 20, 2020
edited by asinus  May 20, 2020

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