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Crocogator

An ordinary 17 year old croc trying to qualify for Regional Mathematical Olympiad.

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  • Member for 1 year, 3 months
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  • Last seen Jan 16 at 13:25

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10 Find a such that $ax^{17}+bx^{16}+1$ is divisible by $x^2-x-1$. Oct 13 '19
5 If $\alpha$, $\beta$, $\gamma$ and $\delta$ be the roots of the polynomial $x^4+px^3+qx^2+rx+s$, prove the following. Oct 12 '19
5 If $\alpha, \beta,\gamma$ be the roots of $2x^3+x^2+x+1=0$, show that…? Dec 30 '19
3 If $p, q$ and $r$ are distinct roots of $x^3-x^2+x-2=0$, find the value of $p^3+q^3+r^3$. Dec 24 '19
3 Why $a^mb^nc^p…$ depends on $\left(\frac{a}{m}\right)^{m}\left(\frac{b}{n}\right)^{n}\left(\frac{c}{p}\right)^{p} \ldots$ for being the greatest? Dec 4 '19
3 Show that $\frac{(2n-1)!}{(n)!(n-1)!}$ is odd or even according as to whether $n$ is or is not a power of $2$. Jan 4 '20
3 Solving the cryptarithm $\mathrm{TWO}+\mathrm{TWO}=\mathrm{FOUR}$ in base $10$ and base $7$ Nov 5 '20
3 For $a \in \mathbb R$, find polynomials $P$ such that $(x^2-ax+18)P(x)-(x^2+3x)P(x-3)=0$ Oct 14 '19
3 Two circles each of which passes through the centre of the other intersect points M and N. Oct 16 '19
2 Find the polynomial equation of the lowest degree with rational coefficients whose one root is…? Oct 11 '19
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