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Question

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If the equation a_nxⁿ +a_n-1x^n-1 +....... +a₁x =0, a₁ ≠ 0, n≥2, has a positive root x = α, then the equation na_nx^n-1 + (n-1)a_n-1x_n-2 +......+a₁ = 0 has a positive root, which is

greater than α

smaller than α

greater than or equal to α

equal to α

Solution

B.

smaller than α

f(0) = 0, f(α) = 0
⇒ f′(k) = 0 for some k∈(0, α).

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