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Question

Question- Let P(x) = xⁿ + a_n-1x^n-1 + a_n-2x^n-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.