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MATH / The polynomials

Problem

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problem

The polynomials x3+5x2+px+q=0x^3 + 5x^2 + px + q = 0and x3+x2+px+r=0x^3 + x^2 + px + r = 0have exactly two roots in common, so each cubic has a root they do not have in common. Find the sum of the two roots they do not have in common.
Plain-text mathematical notation (without MathML)
The polynomials
x³+5x²+px+q=0and
x³+x²+px+r=0have exactly two roots in common, so each cubic has a root they do not have in common.  Find the sum of the two roots they do not have in common.
Original LaTeX notation
The polynomials
\[x^3 + 5x^2 + px + q = 0\]and
\[x^3 + x^2 + px + r = 0\]have exactly two roots in common, so each cubic has a root they do not have in common.  Find the sum of the two roots they do not have in common.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
2dce5c2a-7dd9-5b36-9257-607dae41e7c5
task_key
intermediate~5falgebra--test--2dce5c2a-7dd9-5b36-9257-607dae41e7c5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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