The root of the equation is the value of the unknown that makes the left and right sides of the equation equal. The root and solution of a quadratic equation are different. The root can be multiple, but the solution must be different. If a quadratic equation has two different roots, it is also called two different solutions.

Common methods to prove the existence of roots

1, the zero theorem of continuous function (including generalized zero theorem);

2. Rolle theorem (including generalized zero theorem).

Common methods to prove the uniqueness of heel

1, monotonicity;

2. The inference of Rolle theorem.

Extended data

1, if the conditions and conclusions in the problem involve continuous functions, the zero theorem is generally used to explain that there is a root;

2. If the conditions and conclusions in the problem involve derivatives, Rolle's theorem is generally used to explain that there are roots;

3. Monotonicity or Rolle theorem is often used when there are at most a few roots. Of course, you can also use reduction to absurdity to illustrate that there are at most a few roots;

4. Discuss the roots of equation f(x)=0 or equation f(x, k)=0 with parameters on region I, mainly by dividing region I into several monotonous regions by using derivatives and combining the endpoint values.

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