The equations of the highest degree are the equations in which the senior degree of a variable more than 3. There is the general scheme for the solution of the equations of the highest degrees with the whole coefficients.
Instruction
1. It is obvious that if the coefficient at the senior degree of a variable is not equal 1, then it is possible to divide all members of the equation into this coefficient and to receive the given equation therefore at once consider the given equation. The general view of the equation of the highest degree is presented in the drawing.
2. First of all find the whole roots of the equation. The whole roots of the equation of the highest degree are a0 dividers - the free member. For their location display a0 on multipliers (unreliable simple) and serially check what of them are equation roots.
3. When find such x1 which turns a polynomial into zero among dividers of the free member, it is possible to present an initial polynomial in the form of the work of a monomial and a polynomial of degree of n-1. For this purpose the initial polynomial is divided on x - x1 in a column. Now the general view of the equation changed.
4. Further continue to substitute a0 dividers, but already in the turned-out equation of smaller degree. And begin with x1 as the equation of the highest degree can have multiple roots. If there are still roots, then again divide a polynomial into the corresponding monomials. Thus display a polynomial so that to receive as a result the work of monomials and a polynomial of degree 2, 3 or 4.
5. Find roots of a polynomial of younger degree, using the known algorithms. This finding of a discriminant for a quadratic equation, a formula Cardano for the cubic equation and various replacements, transformations and a formula Ferrari for the equations of the fourth degree.