"Solving Quadratic Equations of One Variable" PPT Courseware for Quadratic Equations of One Variable 6

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"Solving Quadratic Equations of One Variable" PPT Courseware for Quadratic Equations of One Variable 6

1. direct square root descending method

According to the definition of square root, a quadratic equation of one variable ______ is transformed into a linear equation of one variable_. This method can solve an equation of the form (x-a)2=b (b≥0), and its solution is_ ___________．

Note: The types of solutions to quadratic equations of one variable using the direct square root method are:

x2=a(a≥0); ax2=b(a, b have the same sign, and a≠0); (x+a)2=b(b≥0);

a(x+b)2=c(a,c have the same sign, and a≠0).

2. Preparation method

The method of solving a quadratic equation of one variable by forming it into _______________ is called

Preparation method. The recipe is to _________, convert a quadratic equation of one variable into _____________ to solve.

Note: General steps for preparation methods:

①Move the constant term to the right side of the equal sign;

② Change the coefficient of the quadratic term to 1;

③Add half the square of the coefficient of the linear term to both sides of the equation.

Summary: It can be seen from the above that

(1) The roots of the quadratic equation ax2+bx+c=0 (a≠0) are determined by a, b, and c of the equation;

(3) The method of using the root formula to solve a quadratic equation of one variable is called the formula method;

(4) It can be seen from the root finding formula that a quadratic equation of one variable has at most two real roots.

Note: When using the formula method, the equation must first be simplified into a general formula.

4. Discriminant of Roots of Quadratic Equation

The equation can be directly judged from the value of the discriminant of the root_______________

The number of roots without solving the equation:

When Δ=b2-4ac>0, the equation ____________________;

When Δ=b2-4ac=0, the equation ____________________;

When Δ=b2-4ac<0, the equation ____________________________.

Use the formula method to solve the following equations:

(1)x2+6x+5=0;

(2)2x2+6x-2=0;

(3)(1+x)2+2(x+1)-4＝0.

Thoughts: General steps for solving quadratic equations of one variable using the combination method:

(1) Change the coefficient of the quadratic term to 1;

(2) Move the terms so that the left side of the equation is a quadratic term and a linear term, and the right side is a constant term;

(3) Formula, add half the square of the coefficient of the linear term to both sides of the equation;

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For more information about the PPT courseware "Quadratic Equations of One Variable and Solving Quadratic Equations of One Variable", please click the "Quadratic Equations of One Variable Equation ppt Solution of Quadratic Equations of One Variable" ppt tag.

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Update Time: 2024-10-19

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

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