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Find all positive integer values of c such that the equation x^2 - 5x + c only has roots that are real and rational. Express them in decreasing order, separated by commas.

Oct 12, 2020

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Find all positive integer values of c such that the equation x^2 - 5x + c only has roots that are real and rational. Express them in decreasing order, separated by commas.

Hello Guest!

$$x^2 - 5x + c =0$$

p        q

$$x=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}$$

$$x=2.5\pm \sqrt{6.25-c}$$

$$c\in \mathbb{N_0}\ |0\le c\le6$$

Oct 12, 2020
edited by asinus  Oct 12, 2020