After the coefficient of the first term of the quadratic equation of one variable is exchanged with the constant term, one root of the new equation is twice as much as one root of the original equation, and the other root is the same as the original equation. Please write such an equation, and you'd better tell me the reason,

The front part of the building is quite reasonable, but there is something wrong with the back part. Let's borrow some expressions^_ ^Let the original univariate quadratic equation be X & # 178; + BX + C = 0, and its roots are x1, x2. Then the new equation is X & # 178; + CX + B = 0, and its roots are 2x1, x2

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1. Given z = 1 − 2I, then 1z=______ ．
2. The real part of complex I is
3. 2. What is the conjugate complex number of the complex number 2I / (1-I), the calculation process, thank you ~~
4. The conjugate complex of complex 2i1 − I is______ ．
5. The conjugate complex of complex number (1-2i) ∧ 2 is
6. In the complex plane, set points a, B and C, and the corresponding complex numbers are I, 1, 4 + 2I respectively. Make a parallelogram ABCD through a, B and C. find the coordinates of point D and the length of the diagonal BD of the parallelogram
7. In the complex plane, set a point A.B.C, and the corresponding complex numbers are I, 1, 4 + 2I respectively. Through a, B, C, make the parallelogram ABCD, and find the length of the diagonal BD of the parallelogram
8. The complex numbers corresponding to points a, B and C in the complex plane are I, I, 4 + 2I respectively. If a - > b - > C - > D is parallelogram ABCD in anticlockwise order, then | BD | is equal to?
9. It is known that the complex numbers of vertices a and B of isosceles trapezoid oabc on the complex plane are 1 + 2I and - 2 + 6I respectively, and O is the origin of coordinates, OA ‖ BC. Find the complex number Z corresponding to vertex C
10. In the complex plane, the complex numbers corresponding to the vertices O and B of the rectangular oabc are 0 and √ 2 (1 + I) respectively And │ OA │ = √ 3, │ OC │ = 1, then the complex numbers corresponding to a and C are______
11. Write out a quadratic equation of one variable with one root of 2 and the other root of 1
12. Write out a quadratic equation with one variable, so that one root is greater than 1, the other root is less than 1, and the equation with quadratic coefficient of 1 is______ ．
13. What is the relationship between the root and the coefficient of the equation of degree n of one variable Quadratic equation of one variable Univariate cubic equation . What does it have to do with coefficient
14. What is the sum of n roots of the equation of degree n in one variable? Can there be a proof process/ One variable n-th path The sum of n roots of XN + an-1xn-1 + ····· + a1x + A0 = 0 is equal to?
15. How to prove that an equation of degree n of one variable must have complex roots
16. Given that a, B and C are the three roots of the equation x ^ 3 + PX + q = 0, how to get a + B + C = 0 according to the relationship between the root and the coefficient Such as the title
17. Should the plural be z = a + bi or Z = a + IB I saw z = a + bi in my high school math textbook But the advanced mathematics book says z = a + IB Which one is right
18. Let A0 + A1 / 2 +. + an / (n + 1) = 0, and prove that the polynomial f (x) = A0 + a1x +. + anx ^ n has at least one zero point in (0,1)
19. It is proved that the polynomial A0 * x ^ n + A1 * x ^ n-1 + A2 * x ^ n-2 +. +... An = 0 has at least one real root when n is odd. (A0! = 0)
20. If the complex sequence {an} satisfies A1 = 0, an = (an-1) ^ 2 + I (n is greater than or equal to 2), then the sum of its first 2007 terms is?