"The relationship between roots and coefficients of quadratic equations" PPT courseware for quadratic equations

Description

"The relationship between roots and coefficients of quadratic equations" PPT courseware for quadratic equations

1. What is the general form of a quadratic equation?

ax²+bx+c=0(a≠0)

2. What is the formula for finding the root of a quadratic equation?

x=-b±√b²-4ac/2a b²-4ac≥0

3. How to determine the roots of a quadratic equation?

4. Find a quadratic equation of one variable such that its two roots are

①2 and 3; ②-4 and 7; ③3 and -8; ④-5 and -2

①(x-2)(x-3)=0 x²-5x+6=0

②(x+4)(x-7)=0 x²-3x-28=0

③(x-3)(x+8)=0 x²+5x-24=0

④(x+5)(x+2)=0 x²+7x+10=0

Question 1: From the process of solving these equations, what relationship did you find between the roots and the coefficients?

If the equation x²+px+q=0 has two roots, they are x1, x2

Then we have x1+ x2=-p, x1 •x2=q

Conjecture: 2x²-5x+3=0, what is the relationship between the sum of the two roots of this equation, the product of the two roots, and the coefficients?

When finding the value of an algebraic expression related to the roots of an equation, the algebraic expression is generally first converted into a form containing the sum of two roots and the product of two roots, and then substituted as a whole.

basic exercises

1. If -1 is a root of the equation 2X²-X+m=0, then the other root is ___, m =____.

2. Suppose X1 and X2 are the two roots of the equation X²-4X+1=0, then

X1+X2 = ___,X1X2 =____,

X1²+X2² = ( X1+X2)² -___ =___

(X1-X2)² = ( ___ )2- 4X1X2 = ___

3. Check whether it is true or false: The equation with 2 and -3 as roots is X²-X-6=0 ( )

4. It is known that the sum of two numbers is 1 and the product is -2, then the two numbers are _____.

practise:

(1) If one root of the equation 2x²+5x+n=0 about x is -2, find its other root and the value of n.

(2) If one root of the equation x²+kx-6=0 about x is -2, find its other root and the value of k.

Summary

1. What is the relationship between the roots and coefficients of a quadratic equation?

2. When applying the relationship between the roots and coefficients of a quadratic equation, the known equation must first be transformed into a general form.

3. When applying the relationship between the roots and coefficients of a quadratic equation of one variable, special attention should be paid to the condition that the equation has real roots, that is, in junior high school algebra, the relationship between the roots and coefficients can be applied if and only if b²-4ac≥0.

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For more information about the PPT courseware "The relationship between the roots and coefficients of a quadratic equation", please click the "Quadratic equation ppt The relationship between the roots and coefficients of a quadratic equation ppt" tag.

"The relationship between roots and coefficients of quadratic equations" PPT courseware for quadratic equations 2:

"The relationship between the roots and coefficients of a quadratic equation" PPT courseware for quadratic equations 2 Knowledge points: The relationship between the roots and coefficients of a quadratic equation 1. The sum of the two real roots of the following quadratic equation of one variable is -4 ( ) A. x+2x-4＝0 B． x-4x+4＝0 C． x..

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Update Time: 2024-09-12

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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