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Using Ruler and Compass we can construct any solution to a quadratic equation.

I am wondering whether the idea can be generalized to construct solutions to higher order polynomials.

For example can quadratic curves and compass construct any solution to a cubic, cubic curves and compass construct any solution to a quartic, and so on?

Alternatively can one use a ruler and some alternative transcendental curve to solve higher order polynomials?

YeatsL
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1 Answers1

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Using conics (which are quadratic curves), we can solve any cubic and quartic equation with rational coefficients.

José Carlos Santos
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