If the equation

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

If the equation anxn+an−1xn−1+⋯+a1x=0a_nx^n+a_{n-1}x^{n-1}+\dots+a_1x=0, where a1≠0a_1\ne0 and n≥2n\geq2, has a positive root x=αx=\alpha, then the equation nanxn−1+(n−1)an−1xn−2+⋯+a1=0na_nx^{n-1}+(n-1)a_{n-1}x^{n-2}+\dots+a_1=0 has a positive root which is (1) greater than or equal to α\alpha (2) equal to α\alpha (3) greater than α\alpha (4) smaller than α\alpha

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