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Regardless of version period: 346
This week's teaching content: an overview of Vieta's theorem and its application. There are two real numbers rooted in the application of Huvier Tower Theorem, so,. These two formulas reflect the relationship between the product of two roots and the sum of two roots and the coefficients A, B and C of a quadratic equation with one variable, which is called the Wietta theorem. Its inverse proposition also holds. Vieta's theorem and its inverse theorem, as an important theory of quadratic equation with one variable, are widely used in junior high school mathematics competitions. This lecture focuses on its application in five aspects. Key points 1. Find the value of algebraic expression ★★★ Example 1 If A and B are real numbers, and, find the value of. Note that a and b are equations). Solution (1) When a=b,; (2) When A and B are equations respectively, ab= 1. It shows that this problem is easy to miss the solution of A = B .. the symmetric polynomial of the root, etc. It can be expressed by the coefficient of the equation. Generally speaking, let is the two roots of the equation, and then there is a recursive relationship. Where n is a natural number. This relationship can solve many competitive problems. Polynomial values are found for values a and b, but the amount of calculation is large. 2 If, and, try to find the value of the algebraic expression. This example can be solved by the recursive formula explained in the above example, or by algebraic deformation. Solution: Because M and N are equations derived from the definition of roots, Vieta's theorem is applicable to ∴ 2. Constructing a quadratic equation in one variable Example 3 Let the two real roots of the quadratic equation in one variable be sum. (1) Try to find the root of a quadratic equation with one variable; (2) If
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Discriminating Vieta Theorem
(2) When B2-4ac = 0, Vieta's theorem, _ _ _ _ _ _.
(3) When B2-4ac is less than 0, _ _ _ _ _
3. Let x 1 and x2 be the two roots of the equation ax2+bx+x=0(a≠0), then x1+x2 = _ _ _ _ _ _
x 1x 2 = _ _ _ _ _ _ _ _ _ _ _ _ _ x 12+x22 = _ _ _ _ _ _ _ | x 1-x2 | = _ _ _ _ _ _ _ _
4. The quadratic equation with x 1 and x2 as roots is _ _ _ _ _
Third, basic training.
1, quadratic equation x2-2x+2=0 △ = _ _
2. Discriminant△ = _ _ _ of equation x2-4x+m=0. When m _ _ _ _, the equation has two unequal real roots, when m _ _ _, the equation has two equal real roots, and when m _ _ _, the equation has no real roots.
3. The sum of the two elements of the equation 2x2-8x+3= is _ _ _ _, and the product of the two elements is _ _ _ _.
4. If one root of the equation 5x2+BX- 10 = 0 is 5, the other root is _ _, and b = _ _.
5. If the two roots of the equation x2+px+q=0 are-1 and 3, then p = _ _ p = _ _ _
6, respectively-1 and 5, the two quadratic equations are _ _ _ _ _
7.α and β are two roots of equation y2-3x- 1=0, and the formula of Vieta theorem is α 2+β 2 = _ _+= _ _.
(α-β)2=____
8. Equation 2x2+MX+(2m-1) = 2 of 0
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Veda. document
..... Vedas
Vedas (1540- 1603), a French mathematician, studied law as a lawyer when he was young, then engaged in political activities and served as a member of parliament, deciphering the enemy's code for the government in the war against Spain. The Vedas also devoted themselves to mathematical research, and were the first person who consciously and systematically used letters to represent known numbers, unknown numbers and their power. Great progress has been made in the theoretical research of algebra. David discussed various rational transformations of the roots of the equation, and found the relationship between the roots of the equation and the coefficients (so people call the conclusion describing the relationship between the roots and the coefficients of a quadratic equation in one variable "Vieta Theorem"). David is known as the "father of algebra" in Europe. 100000000005, David published the mathematical law applied to triangles, which was the first plane and sphere in Europe to use six trigonometric functions. His main works include Introduction to Analytical Methods (159 1), On the Identification and Correction of Equations, Five Chapters of Analysis, Mathematical Laws Applied to Triangles, etc. Because David has made many important contributions, he has made many contributions.
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Two momentum theorems. ppt
..... momentum theorem making: Chen Unit: Chaohu No.4 Middle School * Teaching objective 1, to understand the exact meaning and expression of momentum theorem; Know that momentum theorem is applicable to variable force; 2, will use momentum theorem to explain some phenomena and deal with related problems; Second, the significance and application of momentum theorem; Review questions: 1. What is impulse? What about size, direction and unit? 2. What is momentum? What about size, direction and unit? 3. What is momentum change? What about size, direction and unit? Introduction of new lesson to continue new lesson teaching (1), momentum theorem 1, derivation and content: 2. Key points of understanding momentum theorem: (1), formula 1 of momentum theorem =⊿P is a vector momentum theorem ppt, which not only reflects the relationship between the impulse of external force on an object and the change of momentum of the object, but also reflects the relationship between them. (2) Momentum theorem is not only applicable to constant force, but also to variable force. [For the case of variable force, (f) in the momentum theorem should be understood as the average value of variable force within the action time]; (3) In the momentum theorem, I =F = t is the impulse of the combined external force, and ⊿P is the momentum change of the object; (4) The momentum theorem is based on f = m a = m (v'-v)/t f =(P'-P)/t, that is, f =⊿P/t, which is another expression of Newton's second law. The momentum theorem is that the resultant force acting on an object is equal to the rate of change of the momentum of the object. (2) Application of momentum theorem: 1. Momentum theorem can qualitatively explain some phenomena, such as: (1), eggs.
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Cosine Theorem and Its Application 1 Courseware Courseware 2
...... think about it: 1. Please describe the content of sine theorem. Answer: (1) The courseware of cosine theorem of two angles and either side is known. 2. What kinds of problems about triangles can be solved by sine theorem? Find the other two faces and an angle; (2) Knowing the diagonal of two sides and one of them, find the other sides and the angle C B A a b c △ABC. If ∠C is a right angle, C2 = A2+B2A/A/ As shown in the figure: In δ ABC, the lengths of AB, BC and CA are C and A respectively. B: AC = AB+BC = C2-2AC COSB+A2 ∴ AC AC = (AB+BC) (AB+BC), that is, B2 = C2-2AC COSB+A2. It can also be proved that A2 = B2+C2-2bcXhosa C2 = A2+B2-2AB COSB ABC. Bc+bc2 = ab2+2ab bccos (180o-b)+bc2 cosine theorem: the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the cosine product of the included angle between these two sides. Namely: A2 = B2+C2-2bcossab2 = A2+C2-2accosbc2 = A2+B2-2abcosc Note: 1, be familiar with the formal structural features of the theorem, and pay attention to "square", "included angle" and "cosine". 2. Each equation contains four quantities, namely three sides and an angle of a triangle. When ∠ C = 90, then COSC = 0, ∴ C2 = A2+B2, that is, cosine theorem is a generalization of Pythagorean theorem, and Pythagorean theorem in sine and cosine theorem courseware is a special case of cosine theorem: the square of either side of a triangle is equal to twice the product of the sum of the squares of the other two sides minus the cosine of the included angle between the two sides. Namely: a2=b2+
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