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ax^4+bx^3+cx^2+dx+e=0 has at least one real root [Greece 1995]

Source: Greece 1995

February 11, 2009
algebra unsolvedalgebra

Problem Statement

If the equation ax2+(c−b)x+(e−d)=0 ax^2+(c-b)x+(e-d)=0 has real roots greater than 11, prove that the equation ax4+bx3+cx2+dx+e=0ax^4+bx^3+cx^2+dx+e=0 has at least one real root.
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