Roots of quartic equation

What is it about?

This note presents a new method to determine the roots of a quartic polynomial. In this method, the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point, say $(r,0)$. Hence the root, $r$, satisfies both the quartic and the quadratic equations. Elimination of $r$ from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression of our choice in one unknown, to enable us to determine the two unknowns from the two expressions; and subsequently the roots of quartic polynomial are determined.

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