Question: Let a 0 , a 1 , a 2 , a 3 , a 4 be constant real numbers such that a 0 5 a

Let a0,a1,a2,a3,a4 be constant real numbers such that
a05a14a23a12a4=0
Show that the polynomial P(x)=a0x4a1x3a2x2a3xa4 has at least one zero between 0 and 1.(Hint: Consider
f(x)=05x514x423x332x3a4x
Show that Rolle's theorem applies to f(x) on the interval 0,1. Deduce that P(x) has a 0 in (0,1].
Let a 0 , a 1 , a 2 , a 3 , a 4 be constant real

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