Test Academy | A polynomial ψ(s) = a n s n + a n-1 s n-1 + ......+ a 1 s + a 0 of degree n > 3 with constant real coefficients a n , a n-1 , ... a 0 has triple roots at s = -σ. Which one of the following conditions must be satisfied? ψ(s) = 0 at all the three values of s satisfying s3 + σ3 = 0, ψ(s) = 0, d ψ ( s ) d s = 0 and d 2 ψ ( s ) d s 2 = 0 at s = -σ, ψ(s) = 0, d 2 ψ ( s ) d s 2 = 0 and d 4 ψ ( s ) d s 4 = 0 at s = -σ, ψ(s) = 0, d 3 ψ ( s ) d s 3 = 0 at s = -σ

Question

A polynomial ψ(s) = a_nsⁿ + a_n-1s^n-1 + ......+ a₁s + a₀ of degree n > 3 with constant real coefficients a_n, a_n-1, ... a₀ has triple roots at s = -σ. Which one of the following conditions must be satisfied?

Options :

ψ(s) = 0 at all the three values of s satisfying s³ + σ³= 0
ψ(s) = 0, $\frac{d ψ (s)}{d s} = 0$ and $\frac{d^{2} ψ (s)}{d s^{2}} = 0$ at s = -σ
ψ(s) = 0, $\frac{d^{2} ψ (s)}{d s^{2}} = 0$ and $\frac{d^{4} ψ (s)}{d s^{4}} = 0$ at s = -σ
ψ(s) = 0, $\frac{d^{3} ψ (s)}{d s^{3}} = 0$ at s = -σ

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