/sci/ - Science & Math

>>11043930

[math]
\text{Let }P(x)\text{ be a polynomial of degree }n\text{ such that }P(x)=Q(x)P''(x)\text{, where}
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Q(x)\text{ is a quadratic polynomial and }P''(x)\text{ is the second derivative of }P(x)\text{.}
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\text{Show that if }P(x)\text{ has at least two distinct roots then it must have }n\text{ distinct}
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\text{roots.}
[/math]