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# HELP ASAP

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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!

$$kx^2+20x+k=0$$

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

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

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

!

May 20, 2020
edited by asinus  May 20, 2020