Roots of polynomial

Prove that if the equation

a_{0}x^{n} + a_{1}x^{n-1} + ... + a_{n-1}x = 0

has a positive root x₀ then the equation

na_{0}x^{n-1} + (n-1)a_{1}x^{n-2} + ... + a_{n-1} = 0

has a positive root less than x₀

1 Answers

1357

Manish Shankar ·2013-02-04 21:58:28

Think of it like this
one root is x=0 and another is x=x₀

Now try to draw the graph from x=0 to x=x₀

So at one point the curve will change sign, that is f'(x) will become zero.

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