![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Write out a quadratic equation of one variable with one root of 1 and the other root of 27
x2-28x+27
Write a quadratic equation of one variable with negative roots 2 and 1
RT
（x+2)(x-1)=0
After the coefficient of the first order term of a quadratic equation with one variable is exchanged with the constant term, one root of the new equation is twice that of the original equation, and the other root is equal to the original equation
The original equation AX ^ 2 + BX + C = 0, the root is x1, X2, there are X1 + x2 = - B / A, x1x2 = C / A
The new equation AX ^ 2 + CX + B = 0, the root is 2x1, X2, there are 2x1 + x2 = - C / A, 2x1x2 = B / A
So x1x1 = C / a = B / (2a), B = 2C
So X1 + x2 = - 2C / A
2x1+x2=-c/a
The subtraction of the two formulas is: X1 = C / A, X2 = - 3C / A
x1x2=-3(c/a)^2=c/a
We get: C = - A / 3, so B = 2C = - 2A / 3
So the original equation is ax ^ 2-2ax / 3-A / 3 = 0
Taking a = 3, we can get 3x ^ 2-2x-1 = 0
RELATED INFORMATIONS
- 1. The real part and imaginary part of complex number (3 + I) / (2i-1) are_______________ ；_________________ .
- 2. What is the high flame retardant tape for wires and cables? How to use it? What are the structures of ZA, ZB and ZC flame retardant parts?
- 3. Given | x-3 | + | 2y-8 | + | Z-2 | = 0, find the value of the algebraic formula x + 3y-z
- 4. Given: - x + 3Y = 5, find the value of 5 (x-3y) square-8 (x-3y) - 5
- 5. Given - x + 3Y = 5, find the value of 5 (x-3y) &# - 8 (x-3y) - 5
- 6. Given i4x + 3y-5i + ix-2y-4i = 0, find the value of X, y
- 7. Given x-2y / 3y-x = 2 / 3, then the value of Y / X is
- 8. If Z ^ 2 + Z + 1 = 0, find (1 + Z) * (1 + Z ^ 2) * (1 + Z ^ 4) * (1 + Z ^ 8) （1+z^1 If Z ^ 2 + Z + 1 = 0, find (1 + Z) * (1 + Z ^ 2) * (1 + Z ^ 4) * (1 + Z ^ 8) ）… (1 + Z ^ 1024)
- 9. (x+3):(2y-1):(z\2+2)=2:3:4 3-2y+z=8
- 10. 15 and 45, 16 and 72, 1 and 8, 33 and 22, 8 and 9, 3 and 15
- 11. Can Newton's iterative method be used to find all roots of equation of degree n with one variable For example, for a cubic equation with one variable, if the three roots are different, only one real root can be found by Newton iteration method. How can the other two roots be found? If there are complex roots, can we find them? But the iterative method is to find the numerical solution, and sometimes the equation is transcendental equation, can not do polynomial division.
- 12. Given that a, B and C are the roots of the equation x ^ 3 + PX + q = 0, find a + B + C =?, and give the process and theoretical basis, It seems to have something to do with Veda's theorem, but I don't know how to use it But the answer is 0,
- 13. Polynomial f (x) = A0 + a1x + a2x ^ 2 +... + anx ^ n, it is proved that f (x) = 0 has n + 1 different roots, then f (x) is equal to 0
- 14. 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)
- 15. If the complex number sequence {an} satisfies A1 = 0, an = [a (subscript) n-1] ^ 2 + I (n > = 2, I is an imaginary unit), then the sum of its first 2007 terms is Detailed process
- 16. What is the complex number conjugate with itself? What is the complex number conjugate with its square?
- 17. The module of Z = 1-I is equal to____ The main value of the angle is____ Its conjugate complex number is___
- 18. If | Z-1 | = 1, try to explain the locus of the point corresponding to the complex Z
- 19. Given that in the complex plane, the moving point Z corresponds to the complex z = x + Yi, then what graph is the set of points Z satisfying the equation Z ˉ 2 = 1
- 20. In the complex plane, which quadrant is the point corresponding to complex number (1-I) / I?