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Proof: Equation when δ b 2-4ac 0.
ax^2+bx+c=0(a≠0)
There are two solid roots, set to x1, x2
From the root finding formula x (-b δ 2a, you may wish to take it.
x1 (-b- δ 2a, x2 (-b+ δ 2a, then: x1+x2(-b- δ 2a+(-b+ δ 2a
2b/2ab/a,x1*x2=[(-b-√δ/2a][(b+√δ/2a][(b)^2-δ]/4a^2
4ac/4a^2
c/a.In summary, x1+x2=-b a, x1*x2=c a
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The formula for finding the root from a quadratic equation is: x = (-b b 2-4ac) 2a Note: a is the quadratic coefficient, b is the primary coefficient, and c is a constant) can be obtained x1= (-b+ b 2-4ac) 2a , x2= (-b- b 2-4ac) 2a
1. x1﹢x2=(-b+√b^2-4ac)/2a+(-b-√b^2-4ac)/2a
So x1 x2=-b a
2. x1x2= [(b+√b^2-4ac﹚÷2a]×[b-√b^2-4ac﹚÷2a]
So x1x2=c a
Refer to the encyclopedia, and you can ask questions if you have questions.
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a(x-x1)(x-x2)=ax 2-a(x1+x2)x+ax1x2 and a(x-x1)(x-x2)=ax 2+bx+c, so ax 2-a(x1+x2)x+ax1x2=x 2+bx+cThe coefficients of x 2 should be equal (a=a), the coefficients of x should be equal (-a(x1+x2)=b), and the constant term coefficients should be equal (ax1x2=c).
x1x2=c/a
This should work.
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The formula of the violation theorem is shown in the figure below
Vedder's theorem explains the relationship between roots and coefficients in a quadratic equation. The French mathematician François Veda established the relationship between the roots of equations and the coefficients in his book "On the Identification and Revision of Equations" and proposed this theorem. Because Veda first developed this relationship between the roots and the coefficients of modern number equations, people call this relationship Veda's theorem.
A Brief History of Development: François Veda The French mathematician François Veda improved it in his book On the Identification and Revision of Equations.
The solution of the third and fourth equations, and also for the case of n, establishes the relationship between the root of the equation and the coefficients, which is called the Vedic theorem in modern times.
Vedic was the first to discover this relationship between the roots and coefficients of modern number equations, so people call this relationship Veder's theorem. Veda arrived at this theorem in the 16th century, and proved it by relying on the fundamental theorem of algebra, which was only made by Gauss in 1799.
The discriminant formula of the root is a sufficient and necessary condition for determining whether an equation has a real root, and Veda's theorem explains the relationship between the root and the coefficient. Regardless of whether the equation has a real root or not, the relationship between the root of a quadratic equation with real coefficients and the coefficients fits Vedica's theorem. The combination of the discriminant formula and Vedic theorem can more effectively explain the condition and characteristics of the root of the unary quadratic equation determined by the bright band.
The most important contribution of Vedder's theorem was the advancement of algebra, which was the first to systematically introduce algebraic notation, advanced the development of equation theory, replaced unknown numbers with letters, and pointed out the relationship between roots and coefficients. Vedic theorem lays the foundation for the study of unary equations in mathematics, and creates and opens up a wide range of development space for the application of unary equations.
The relationship between the roots of two equations can be quickly found by using Vedder's theorem, which is widely used in elementary mathematics, analytic geometry, plane geometry, and equation theory.
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The Vedic theorem proves the relationship between roots and coefficients in a one-dimensional nth order equation of comic liquids.
Here we talk about the relationship between the two roots of the one-dimensional two-mountain jujube equation. Rock void.
In the unary quadratic equation ax 2+bx+c=0 a≠0, the two x1 and x2 have the following relationship: x1+x2=-b a, x1*x2=c a
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Polar Continent Hidden Color Except B
Live b divides a to fill the father.
That is, the early light hall (x1 times x2) is equal to c key cons a; x1+x2=-b a is a personal memory of the oral decision, in fact, the formula does not have to be memorized, you can make up some oral decisions yourself, I hope it can help you.
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Unary quadratic equation ax 2+bx+c=0 (a is not equal to 0).
The two x1 and x2 of the equation and the coefficients a, b, c of the circular equation satisfy the positive mode x1+x2=-(b a),x1*x2=c orange clear bond a (Vedic theorem).
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