Veda's theorem (relation between root and coefficient) If X1 and X2 are two parts of the equation AX ^ 2 + BX + C = 0 1. Two positive roots 2. Two negative roots 3. One positive root and one negative root Both are bigger than one 5. One is bigger than one, and the other is smaller than one 6. One is bigger than 1, and the other is smaller than 0 7. Both of them are between 3 and 4

Veda's theorem (relation between root and coefficient) If X1 and X2 are two parts of the equation AX ^ 2 + BX + C = 0 1. Two positive roots 2. Two negative roots 3. One positive root and one negative root Both are bigger than one 5. One is bigger than one, and the other is smaller than one 6. One is bigger than 1, and the other is smaller than 0 7. Both of them are between 3 and 4

1.-b/a>0,c/a>0
2.b/a>0,c/a0,b*b-4ac>0,3< -b/(2a)

What is the virtual root pairing theorem of coefficient equation

If Z is the root of real coefficient polynomial f (x), then the conjugate of Z is also the root of F (x) (with the same multiplicity)
The proof is also very simple, just conjugate f (z) = 0

The theoretical significance of the concept of matter

Matter is a philosophical category that marks the objective reality. This objective reality is perceived by human beings through their feelings. It does not depend on our feelings and exists. It is copied, photographed and reflected by our feelings. "This definition of matter contains extremely rich content and has great significance in many aspects
Second, Lenin's definition of material thoroughly adheres to the basic principles of materialism and the monism of materialism. It is a sharp weapon against idealism and dualism
Second, it points out that matter is "perceived by man through his senses", and that man's knowledge can reflect the objective reality. Therefore, it thoroughly adheres to the dialectical materialist theory of reflection and knowability, and points out the direction for people to explore the mysteries of the universe
Thirdly, it makes the highest philosophical generalization of the diversity of the material world, and points out that "objective reality" is the commonness of all materials. It not only affirms the connection between the philosophical material category and the material structure theory of natural science, but also distinguishes them, so as to overcome the defects of metaphysical materialism