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How many roots of the equation {({x}-{1})}{({x}-{2})}{({x}-{3}
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How many roots of the equation \displaystyle{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}+{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}+{\left({x}-{2}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}+{\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}={0} are positive?

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How many roots of the equation \displaystyle{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}+{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}+{\left({x}-{2}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}+{\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}={0} are positive?
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How many roots of the equation \displaystyle{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}+{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}+{\left({x}-{2}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}+{\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}={0} are positive?