Find a bound on the roots of the polynomial

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Question- Let P(x) = xn + an-1xn-1 + an-2xn-2 + ··· + a1x + a0 and T:= 1 + max(0≤i≤n-1) |ai|.

a) Show that if |x| ≥ T, then |P(x)| ≥ 1.

b) Find a bound on the roots of the polynomial P(x) = -7x4 + 2x3 - 3x2 + 4x +5 and relate it to the actual values of the roots.

Reference no: EM13898038

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