"Solving quadratic equations of one variable using formula method" PPT courseware 3

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"Solving quadratic equations of one variable using formula method" PPT courseware 3

We reused the same computational steps for each specific quadratic equation;

Can you use these calculation steps for the general form of the quadratic equation ax²+bx+c=0(a≠0) to find the formula to solve x.

Use this formula to find the solution to each specific quadratic equation and achieve twice the result with half the effort.

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Solve the general form of quadratic equations of one variable using the formula method

ax²+bx+c=0（a≠0）

The root formula of the quadratic equation ax²+bx+c=0:

x=-b±√b²-4ac/2a(b²-4ac≥0)

Using this formula, we can directly obtain the solution of the equation from the values ​​of the coefficients a, b, and c in the quadratic equation. This method of solving equations is called the formula method.

Example 1 Solve the equation: x²-7x-18=0

Solution: ∵a=1, b=-7, c=-18

∵b²-4ac=(-7)²-4×1×(-18)=121

∴x=-b±√b²-4ac/2a=-(-7)±√121/2×1=7 ± 11/2

That is: x1=9 x2=-2

Summary

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

1. Put the equation into a general form.

2. Write the values ​​of a, b, and c.

3. Find the value of b²-4ac.

Special note: If b²-4ac＜0, the equation has no solution

4. Substitute the root formula: x=-b±√b²-4ac/2a

5. Write the solution to the equation: x1x2

According to the sign of the value of b²-4ac, the roots of the quadratic equation ax²+bx+c=0 can be determined,

So we call b²-4ac the discriminant of the roots of the quadratic equation ax²+bx+c=0.

The roots of the quadratic equation ax²+bx+c=0(a≠0) can be determined by b²-4ac:

When △>0, the equation has two unequal real roots,

When △ = 0, there are two equal real roots,

When △<0, there are no real roots.

The equation m²x²+(2m+1)x+1=0 about x has two unequal real roots, then m_______

Variation 1: The equation m²x²+(2m+1)x+1=0 about x has two equal real roots, then m________

2: The equation m²x²+(2m+1)x+1=0 about x has no real roots, then m_______

3: The equation m²x²+(2m+1)x+1=0 about x has two real roots, then m= ________

4: The equation m²x²+(2m+1)x+1=0 about x has real roots, then m= ________

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"Solving quadratic equations of one variable using formula method" PPT courseware 2:

"Using the formula method to solve quadratic equations" PPT courseware 2 1. Use the formula method to solve the following equation 2x-12x+5=0 2. What are the steps to use the formula method to solve the quadratic equation? 1. If the coefficient of the quadratic term is not 1, change the coefficient of the quadratic term to 1 (divide both sides of the equation by the quadratic term...

"Solving quadratic equations of one variable using formula method" PPT courseware:

"Using the formula method to solve quadratic equations of one variable" PPT courseware formula method is produced like this. Can you use the formula method to solve the equation ax+bx+c=0(a0)? 1. Transform 1: Change the coefficient of the quadratic term to 1 ; 2. Transposition: Move the constant term to the right side of the equation; 3. Formula: Add once to both sides of the equation.

"Solving quadratic equations of one variable using formula method" PPT courseware of quadratic equations of one variable:

"Solving quadratic equations of one variable using the formula method" PPT courseware for quadratic equations of one variable Review and review 1. Use the formula method to solve the following equation 2x-12x+10=0 2. What are the steps to use the formula to solve the quadratic equation of one variable? 1. Change to 1: Change the coefficient of the quadratic term to 1 (divide both sides of the equation by...

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Update Time: 2024-07-11

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