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MATH / Let a and b be real numbers. Let r, s, and t be the roots of f(x)=x³+ax²+bx−1,and then let g(x)=x³+mx²+nx+p be a polynomial with roots r², s², and t². If g(−1)=−5, find the greates…

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problem

Let aa and bb be real numbers. Let r,r, s,s, and tt be the roots of f(x)=x3+ax2+bx−1,f(x) = x^3 + ax^2 + bx - 1,and then let g(x)=x3+mx2+nx+pg(x) = x^3 + mx^2 + nx + p be a polynomial with roots r2,r^2, s2,s^2, and t2.t^2. If g(−1)=−5,g(-1) = -5, find the greatest possible value for b.b.
Plain-text mathematical notation (without MathML)
Let a and b be real numbers. Let r, s, and t be the roots of f(x)=x³+ax²+bx−1,and then let g(x)=x³+mx²+nx+p be a polynomial with roots r², s², and t². If g(−1)=−5, find the greatest possible value for b.
Original LaTeX notation
Let $a$ and $b$ be real numbers. Let $r,$ $s,$ and $t$ be the roots of \[f(x) = x^3 + ax^2 + bx - 1,\]and then let $g(x) = x^3 + mx^2 + nx + p$ be a polynomial with roots $r^2,$ $s^2,$ and $t^2.$ If $g(-1) = -5,$ find the greatest possible value for $b.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
a960ecfb-b7f5-5169-9b07-bebc9525f215
task_key
intermediate~5falgebra--test--a960ecfb-b7f5-5169-9b07-bebc9525f215
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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