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MATH / Find all positive integers k with the following property:

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problem

Find all positive integers kk with the following property: For all positive integers a,a, b,b, and cc that make the roots of ax2+bx+c=0ax^2 + bx + c = 0rational, the roots of 4ax2+12bx+kc=04ax^2 + 12bx + kc = 0 will also be rational. Enter all the possible values of k,k, separated by commas.
Plain-text mathematical notation (without MathML)
Find all positive integers k with the following property:

For all positive integers a, b, and c that make the roots of
ax²+bx+c=0rational, the roots of 4ax²+12bx+kc=0 will also be rational.

Enter all the possible values of k, separated by commas.
Original LaTeX notation
Find all positive integers $k$ with the following property:

For all positive integers $a,$ $b,$ and $c$ that make the roots of
\[ax^2 + bx + c = 0\]rational, the roots of $4ax^2 + 12bx + kc = 0$ will also be rational.

Enter all the possible values of $k,$ separated by commas.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
0a2650fe-57de-5c59-90ec-1e23f860d3c3
task_key
intermediate~5falgebra--test--0a2650fe-57de-5c59-90ec-1e23f860d3c3
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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