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.
+14903 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.
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\(kx^2+20x+k=0 \)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ a=c=k\\ b=20\\ x = {-20 \pm \sqrt{20^2-4k^2} \over 2k}\\ x = {-20 \pm \sqrt{400-4k^2} \over 2k}\)
\(x = {-20 \pm 2\sqrt{100-k^2}\over2k}\)
\(k=\{1,2,3,4,5,6,7,8,9,10\}\)
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