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MATH / What is the largest value of k for which the polynomials Q₁(x)=x²+(k−29)x−k and Q₂(x)=2x²+(2k−43)x+k can both be factors of a cubic polynomial P(x)?

Problem

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problem

What is the largest value of kk for which the polynomials Q1(x)=x2+(k−29)x−kQ_1(x) = x^2 + (k - 29)x - k and Q2(x)=2x2+(2k−43)x+kQ_2(x) = 2x^2 + (2k - 43)x + k can both be factors of a cubic polynomial P(x)P(x)?
Plain-text mathematical notation (without MathML)
What is the largest value of k for which the polynomials Q₁(x)=x²+(k−29)x−k and Q₂(x)=2x²+(2k−43)x+k can both be factors of a cubic polynomial P(x)?
Original LaTeX notation
What is the largest value of $k$ for which the polynomials $Q_1(x) = x^2 + (k - 29)x - k$ and $Q_2(x) = 2x^2 + (2k - 43)x + k$ can both be factors of a cubic polynomial $P(x)$?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
e9135ce4-2e5f-52d5-9c75-8dd2d6a3ed8e
task_key
intermediate~5falgebra--test--e9135ce4-2e5f-52d5-9c75-8dd2d6a3ed8e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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