"Solving Quadratic Equations of One Variable" PPT courseware for quadratic equations of one variable 8

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"Solving Quadratic Equations of One Variable" PPT courseware for quadratic equations of one variable 8

1. How many methods have we learned to solve quadratic equations of one variable?

Direct square root method x²=a (a≥0)

Allocation method (x+m)²=n (n≥0)

2.What is decomposition factor?

The decomposition of a polynomial into the product of several integers is called factorization.

What are the methods of factoring?

(1) Extract common factor method:

am+bm+cm=m(a+b+c).

(2) Formula method:

a²-b²=(a+b)(a-b), a²±2ab+b²=(a±b)².

(3) Cross multiplication method:

x²+(a+b)x+ab=(x+a)(x+b).

The steps to solve a quadratic equation of one variable by factoring are:

1. Set the right side of the equation equal to 0;

2. Factor the left-hand side of the equation into A×B;

3. According to "ab=0, then a=0 or b=0", convert it into two linear equations of one variable.

4. Solve these two linear equations of one variable respectively, and their roots are the roots of the original equation.

my discovery

Generally, when the coefficient of the linear term of a quadratic equation is 0 (ax2+c=0), the direct square root method should be used;

If the constant term is 0 (ax2+bx=0), the factoring method should be used;

If both the linear term coefficient and the constant term are not 0 (ax2+bx+c=0), first convert it into a general formula and see if the integer on one side is easy to factor. If it is easy, you should use the factoring method, otherwise use the formula Law;

However, when the coefficient of the quadratic term is 1 and the coefficient of the linear term is an even number, it is simpler to use the matching method.

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Update Time: 2024-11-24

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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