{"id":8457,"user_id":8,"qa_id":5270,"answer_id":0,"answer":"If a0n+1+a1n+a2n−1+…+an−12+an=0,a0n+1+a1n+a2n−1+…+an−12+an=0, then the maximum possible number of roots of the equation a0xn+a1xn−1+a2xn−2+…+an−1x+a

Quadratic expression

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Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

The answer is $n$ .

Indeed, let $P_{n} (X) = \sum_{k = 0}^{n} a_{n - k} x^{k}$ be the Legendre polynomial of degree $n$ . It is proportional to $\frac{d^{n}}{d x^{n}} (x^{n} (1 - x)^{n})$ . It is well-known that $P_{n}$ has $n$ distinct zeros in the interval $(0, 1)$ , and by orthogonality we have also

\sum k = 0 n a n id="MathJax-Spa n -214" class="mrow" style="margi n : 0px; paddi n g: 0px; border: 0px; fo n t-style: i n herit; fo n t-varia n t: i n herit; fo n t-weight: i n herit; fo n t-stretch: i n herit; li n e-height: n ormal; fo n t-family: i n herit; fo n t-size: 16.65px; vertical-alig n : 0px; box-sizi n g: co n te n t-box; tra n sitio n : n o n e 0s ease

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Quadratic expression

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manpreet Best Answer 2 years ago

manpreet 2 years ago

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