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MATH / Eric and Charles each think of a quadratic polynomial. To their surprise, both…

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problem

Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start x2+4x+⋯x^2+4x+\cdots. The ratio of the discriminant, b2−4acb^2-4ac, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.
Plain-text mathematical notation (without MathML)
Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start x²+4x+⋯. The ratio of the discriminant, b²−4ac, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.
Original LaTeX notation
Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start $x^2+4x+\cdots$. The ratio of the discriminant, $b^2-4ac$, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.

level

Level 5

type

Algebra

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task_id
fa084b17-ba0d-517b-a0cf-c38cef2bf8f2
task_key
algebra--test--fa084b17-ba0d-517b-a0cf-c38cef2bf8f2
task_revision_id
1
config / split
algebra / test

Official source

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