Any Real?

Algebra Level 4

\(P(x) \)and \(Q(x)\) are two polynomials with real coefficients satisfying below conditions:

\((1)\): \(a\) and \(b\) are the roots of \(P(x)\) and \(Q(x)\) respectively.

\((2)\): \(P(b)Q(a)>0\).

Then is there any real \(c\) exists such that \(P(c)=Q(c) \)?

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