MathDB

Let

P(x) = x^4 + ax^3 + bx^2 + cx + d

and

Q(x) = x^2 + px + q

be two real polynomials. Suppose that there exista an interval

(r,s)

of length greater than

2

SUCH THAT BOTH

P(x)

AND

Q(x)

ARE nEGATIVE FOR

X \in (r,s)

and both are positive for

x > s

and

x<r

. Show that there is a real

x_0

such that

P(x_0) < Q(x_0)

Problem Statement