Quadratic equation of one variable is an important concept in mathematics, especially in algebra and geometry.
The following are some main test sites for the quadratic equation of one variable:
Definition and form:
The quadratic equation of one variable refers to the shape of ax? +bx+c=0, where a, b and c are real numbers and a≠0. This is the most basic form, and other complex quadratic equations can be simplified into this form.
Solution:
There are two main methods to solve the quadratic equation of one variable, one is formula method, and the other is factorization method.
Formula method:
The formula for finding the root of a quadratic equation with one variable is x = [-b sqrt (b? -4ac)]/(2a). Where sqrt stands for square root and needs to be calculated by a calculator.
Factorization method:
Factorizing the equation, such as (x+m)(x+n)=0, then the solution of the equation is x=-m or x =-n. This method is intuitive and can be used to solve some practical problems.
Discriminant of roots:
The discriminant of the root of a quadratic equation in one variable is b? -4ac. When the discriminant is less than 0, the equation has no real number solution; When the discriminant is equal to 0, the equation has two equal real number solutions; When the discriminant is greater than 0, the equation has two different real number solutions.
The relationship between root and coefficient:
If the unary quadratic equation has two real roots, x 1 and x2, then x 1+x2=-b/a, X 1 * X2 = C/A, which is a very important relationship and can be used to solve many problems.
Application:
One-dimensional quadratic equation has applications in many fields, such as geometry (using one-dimensional quadratic equation to solve area, perimeter and so on). ), physics (using a quadratic equation to describe the law of motion, etc. ), economics (using a quadratic equation to describe economic growth or recession, etc. ).
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Complex solution:
When the discriminant is less than 0, the solution of the equation is complex. Like when the equation is x? When +5x+6=0, if the discriminant is less than 0, the solution is = [-5 sqrt(-5)]/2, where sqrt(-5) represents -5 under the square root and is a complex number.
One-dimensional higher order equation:
The univariate quadratic equation is the simplest univariate higher order equation. Similarly, we can also define a cubic equation, a quartic equation and so on. The solutions of these equations are similar to those of quadratic equations in one variable, but more complicated.
Nonlinear equation:
The quadratic equation of one variable is a linear equation. If the highest order of the equation is greater than 2, or contains nonlinear terms (such as x? , sin(x), etc. ), then this is a nonlinear equation. The solution of nonlinear equations is usually much more complicated than that of linear equations, which requires special methods and skills.
Application in practical problems;
Quadratic equation with one variable is widely used in social science as well as in mathematics and natural science. For example, in economics, a quadratic equation can be used to describe the balance between supply and demand, the optimal price, the economic growth rate and so on. In computer science, the quadratic equation of one variable is also the basis of optimization algorithm.
Generally speaking, quadratic equation with one variable is an important concept in mathematics, and its definition, solution and application need to be mastered skillfully. Through study and practice, you can gradually master this concept and apply it to a wider range of fields.