1, quadratic equation refers to a one-dimensional integral equation with the highest order of 2, and its general form is ax? +bx+c=0(a≠0). The relationship between roots and coefficients of quadratic equation means that the coefficients A, B, C of quadratic equation can be obtained by knowing three roots of quadratic equation. This relationship was discovered by French mathematician Francois Viete in16th century, so it is also called Vieta theorem.
2. The content of Vieta's theorem is: Let the quadratic equation ax? The two roots of +bx+c=0(a≠0) are α and β respectively, so there are α+β=-b/a and α β = c/a. This theorem is very useful in solving quadratic equation problems and can help us quickly solve the coefficients of quadratic equation.
3. However, Vieta's theorem is not omnipotent. For some special quadratic equations, even if we know its three roots, we can't directly use Vieta's theorem to solve the coefficients. At this time, we need to use other methods to solve it. For example, we can first turn the quadratic equation into a standard form, and then use the discriminant to judge whether it has a real root.
Learning method of solving equations
1. Understand the meaning and importance of equations: Before you start to learn to solve equations, you need to understand the meaning and importance of equations. Equation is a mathematical expression, which contains an equal sign, and both sides of the equal sign are unknown and known respectively. By solving the equation, the value of the unknown quantity can be obtained, thus solving practical problems.
2. Master the basic steps of solving equations: The basic steps of solving equations include: removing brackets, shifting terms, merging similar terms, and transforming coefficients into 1. These steps are the basis of solving equations and need to be mastered skillfully. In the process of learning, you can deepen your understanding of these steps by doing more exercises.
3. Use appropriate mathematical tools: In the process of solving equations, some mathematical tools such as calculators and computer software can help us find the answer quickly and accurately. At the same time, you can also use charts, images and other auxiliary tools to better understand the problem.
4. Pay attention to the ideas and methods of solving problems; In the process of solving equations, we need to pay attention to the ideas and methods of solving problems. For different types of equations, different methods are needed to solve them. For example, a linear equation with one variable can be solved by shifting terms and merging similar terms. For binary linear equations, we can solve them by substitution method and elimination method.