# 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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