For example, the roots of λ 4-2λ 3+λ 2 = 0 are 0,0, 1, 1, and its roots can also be expressed as double roots 0 and double roots 1.

The equation f(x) = 0 has a root x = a, which means that f(x) has a factor (x-a), so we can divide P(x) = f(x)/(x-a) by a polynomial, and the result is still a polynomial. If P(x) = 0 still takes x= a as the root, then x = a is the multiple root of the equation.

Or let f 1(x) be the derivative of f(x). If f 1(x) = 0 is also based on x =a, it can also be explained that x= a is the multiple root of the equation f(x)=0.

Extended data:

The solution of multivariate equation is a set of unknowns. For example, x=2, y= 1 is the solution of the binary equation 2x-y=3. If several of all the roots of an equation are equal, these roots are called multiple roots.

For example, if the unary equation x3(x- 1)2(x+3)=0, its root is x 1=x2=x3=0, x4=x5= 1, x6=-3, then "0" is its triple root, ".

The set of all solutions of an equation is called the solution set of this equation. If the equation has no solution, the solution set is empty. An equation without a solution is called a contradiction equation, so the solution set of a contradiction equation is an empty set.

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