Basic definition
For the function y=f(x), the real number x with f(x)=0 is called the zero point of the function y=f(x), that is, the zero point is not a point.
In this way, the zero point of the function y=f(x) is the real root of the equation f(x)=0, that is, the abscissa of the intersection of the image of the function y=f(x) and the X axis.
Equivalence condition
Equation f(x)=0 has a real number root = the image of function y=f(x) has an intersection with the x axis = function y = f(x) has a zero point.
The method of finding the zero point of function
Finding the real root of equation f(x)=0 is to determine the zero point of function y=f(x). Generally speaking, for the equation f(x)=0 that cannot be solved by the formula, we can relate it with the function y=f(x), and use the properties of the function to find the zero point, so as to find the root of the equation.
The function y=f(x) has zero, that is, y=f(x) has an intersection with the horizontal axis, and the equation f(x)=0 has a real root, so △≥0 can be used to find the coefficient, or it can be combined with the expression of the derivative function to solve the unknown coefficient.