Minimum in bi-quadratic!

Algebra Level 5

If \({ a }_{ i }\) is positive or negative as \(i\) even or odd respectively. If \({ x }^{ 4 }+{ { a }_{ 1 } }{ x }^{ 3 }+{ a }_{ 2 }{ x }^{ 2 }+{ a }_{ 3 }x+5=0\quad \) has four Positive roots the them find minimum value of \({ a }_{ 1 }{ a }_{ 3 }\)

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