Bring Radical
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High Quality Content by WIKIPEDIA articles! George Jerrard (1804 1863) showed that some quintic equations can be solved using radicals and Bring radicals, which had been introduced by Erland Bring (1736 1798). They can be used to obtain closed form solutions of quintic equations.Thhis iteration method produces two roots of the quintic. The remaining three roots can be obtained by using synthetic division to divide the two roots out, producing a cubic equation. It is to be noted that due to the way the iteration is formulated, this method seems to always find two complex conjugate roots of the…mehr

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High Quality Content by WIKIPEDIA articles! George Jerrard (1804 1863) showed that some quintic equations can be solved using radicals and Bring radicals, which had been introduced by Erland Bring (1736 1798). They can be used to obtain closed form solutions of quintic equations.Thhis iteration method produces two roots of the quintic. The remaining three roots can be obtained by using synthetic division to divide the two roots out, producing a cubic equation. It is to be noted that due to the way the iteration is formulated, this method seems to always find two complex conjugate roots of the quintic even when all the quintic coefficients are real and the starting guess is real. This iteration method is derived by from the symmetries of the icosahedron and is closely related to the method Felix Klein describes in his book.