"The relationship between roots and coefficients of quadratic equations" PPT courseware 3

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"The relationship between roots and coefficients of quadratic equations" PPT courseware 3

If the two roots of ax2+bx+c=0 (a≠0) are x1 and x2, then

x1+x2=________, x1·x2=________.

Two conditions should be noted when applying the root-coefficient relationship:

(1)____________________;

(2)____________________.

1. (3 points) (2013·Wuhan) If x1 and x2 are the two roots of the quadratic equation x2-2x-3=0, then the value of x1x2 is ()

A． -2　B. －3　C． 2D． 3

2. (3 points) If x1 and x2 are two roots of the quadratic equation x2-3x+2=0, then the value of x1+x2 is ()

A． -2 B． 2C． 3D． 1

3. (3 points) The sum of the two real roots of the following quadratic equation is -4 ()

A． x2+2x-4＝0 B． x2－4x＋4＝0

C. x2＋4x+10＝0 D. x2+4x-5＝0

4. (3 points) It is known that x1 and x2 are two real roots of the equation x2-4x-5=0, then (x1-2)(x2-2)=______.

【Error-prone Inventory】

[Example] It is known that x1 and x2 are two unequal real roots of the quadratic equation x2-(2m+3)x+m2=0 about x, and satisfy x1+x2=m2, then the value of m is ()

A． -1B． 3

C. 3 or -1 D. -3 or 1

【Incorrect interpretation】C

[Error cause analysis] The value of the undetermined coefficient in the equation obtained from the relationship between roots and coefficients does not pass the Δ=b2-4ac>0 test.

【correct】

11. (5 points) It is known that the two roots of the quadratic equation x2-3x-1=0 are x1 and x2, then the value of xx2+x1x is ()

A． -3B. 3C． -6D. 6

12. (5 points) When solving a quadratic equation of one variable, A misunderstood the constant term of the equation, so the two roots were 8 and 2; B misunderstood the coefficient of the linear term of the equation, so the two roots were -9 or -1, then the correct equation is ()

A． x2－10x＋9＝0 B. x2＋10x+9＝0

C. x2－10x－9=0 D． x2+10x-9=0

15. (10 points) It is known that the two real roots of the quadratic equation x2-2x+m=0 are x1, x2, and x1+3x2=3, find the value of m.

16． (12 points) It is known that the two real roots of the quadratic equation x2=2(1-m)x-m2 about x are x1, x2.

(1) Find the value range of m;

(2) Assume y=x1+x2, when y takes the minimum value, find the corresponding value of m, and find the minimum value.

17． (14 points) It is known that x1 and x2 are two real roots of the quadratic equation (a-6)x2+2ax+a=0.

(1) Is there a real number a such that -x1+x1x2=4+x2 is true? If it exists, find the value of a; if it does not exist, please explain the reason;

(2) Find the integer value of the real number a such that (x1+1)(x2+1) is a negative integer.

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For more information about the "Relationship between Roots and Coefficients of Quadratic Equations" PPT courseware, please click on the "Relationship between Roots and Coefficients of Quadratic Equations" ppt tag.

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

"The Relationship between the Roots and Coefficients of a Quadratic Equation" PPT Courseware 2 Recall 1. What is the general form of a quadratic equation? ax2+bx+c=0 (a0) 2. What is the formula for finding the root of a quadratic equation? x=-bb-4ac/2a(b-4ac0 3. The situation of the roots of the quadratic equation...

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

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Update Time: 2024-09-30

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