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Omni-MATH / Let a and b be real numbers, and let r,s, and t be the roots of f(x)=x³+ax²+bx−1. Also, g(x)=x³+mx²+nx+p has roots r²,s², and t². If g(−1)=−5, find the maximum possible value of b.

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problem

Let aa and bb be real numbers, and let r,sr, s, and tt be the roots of f(x)=x3+ax2+bx−1f(x)=x^{3}+a x^{2}+b x-1. Also, g(x)=x3+mx2+nx+pg(x)=x^{3}+m x^{2}+n x+p has roots r2,s2r^{2}, s^{2}, and t2t^{2}. If g(−1)=−5g(-1)=-5, find the maximum possible value of bb.
Plain-text mathematical notation (without MathML)
Let a and b be real numbers, and let r,s, and t be the roots of f(x)=x³+ax²+bx−1. Also, g(x)=x³+mx²+nx+p has roots r²,s², and t². If g(−1)=−5, find the maximum possible value of b.
Original LaTeX notation
Let $a$ and $b$ be real numbers, and let $r, s$, and $t$ be the roots of $f(x)=x^{3}+a x^{2}+b x-1$. Also, $g(x)=x^{3}+m x^{2}+n x+p$ has roots $r^{2}, s^{2}$, and $t^{2}$. If $g(-1)=-5$, find the maximum possible value of $b$.

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Source and history

task_id
27c12db7-b372-5c7f-bcf0-6ddaf2068886
task_key
test--27c12db7-b372-5c7f-bcf0-6ddaf2068886
task_revision_id
1
config / split
/ test

Official source

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