Let a0, a1, a2, a3, a4 be constant real numbers such thata0/5 + a1/4 + a2/3 + a3/2 + a4 = 0.Show that the polynomial P (x) = a0x^4 + a1x^3 + a2x^2 + a3x + a4 has at least one zero between0 and 1. (Hint: Considerf (x) = a0/5 x^5 + a1/4 x^4 + a2/3 x^3 + a3/2 x^2 + a4x.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 a0, a1, a2, a3, a4 be constant real numbers such that
a0/5 + a1/4 + a2/3 + a3/2 + a4 = 0.
Show that the polynomial P (x) = a0x^4 + a1x^3 + a2x^2 + a3x + a4 has at least one zero between
0 and 1. (Hint: Consider
f (x) = a0/5 x^5 + a1/4 x^4 + a2/3 x^3 + a3/2 x^2 + a4x.
Show that Rolle’s theorem applies to f (x) on the interval [0, 1]. Deduce that P (x) has a 0 in
[0, 1]).