<h1 class="pgc-h-arrow-right" data-track="1" > preface</h1>
If you have a headache about solving unary quadratic equations, then you may wish to take a look at this article, starting from the simplest unary quadratic equations, classifying them, from easy to difficult, and gradually learning the solution of unary quadratic equations.
<h1 class="pgc-h-arrow-right" data-track="3" > starts with the definition and solution of unary quadratic equations</h1>
1. Definitions
The standard form of a unary quadratic equation is ax^2 +bx+c=0(a≠0), because it contains only an unknown, it is called "unary", "yuan" is the meaning of unknown, because the highest number of times is 2, so the left side of the equation is a quadratic polynomial, the equation is a "quadratic" equation, so equations such as ax^2+bx+c=0 (a≠0) are called unary quadratic equations.
2. Solution
The basic idea is to reduce the order, to reduce the number of unary quadratic equations into unary quadratic equations. There are two ideas for descending, one is to use the square root, and the other is to use the factor decomposition.
(1) The square root is reduced
From x^2=2, we can get x=±√2, and then we can think that as long as the unary quadratic equation is converted into the square equal to a few points of the x term, we can smoothly descend and solve.
(2) Factorization decreases
For the equation (x+1) (x-2) = 0, from 0 multiplied by any number to get 0, when x + 1 = 0 or x -2 = 0 when the equation is true, and then to find x1 = -1, x2 = 2, the same we can think of, as long as the unary quadratic equation is converted into the form of the product of several factors of 0, you can smoothly descend and solve.
The method obtained by using the idea one is the direct square and matching method, and the method obtained by using the idea two is the factorization method.
<h1 class="pgc-h-arrow-right" data-track="13" >uniary quadratic equation of the missing term class and its optimal solution</h1>
In the unary quadratic equation ax^2 +bx+c=0(a≠0), a ≠0, but b and c can be 0.
1. Missing primary term and constant term (ax^2=0)
Directly squared, x1=x2=0
2. Missing primary term (ax^2+c=0)
Square directly
Example 1, 2x^2-3=0
Example 2 (Example 1 variant), 2 (x+1) ^2-3=0
3. Missing constant term (ax^2+bx=0)
Factorization method
Example 3, 2x^2+3x=0
Example 4 (example 3 variant), 2 (x+1)^2+3(x+1) = 0