How do you know the root of a cubic equation with one variable to solve the other two roots? For example: knowing one root X1 of the equation f (x) = x ^ 3 + ax ^ 2 + BX + C = 0, how to find the other two roots x2 and X3~

How do you know the root of a cubic equation with one variable to solve the other two roots? For example: knowing one root X1 of the equation f (x) = x ^ 3 + ax ^ 2 + BX + C = 0, how to find the other two roots x2 and X3~

We can find (x ^ 3 + ax ^ 2 + BX + C) / (x-x1) by integral division and get a quadratic equation
Solving the quadratic equation, we can get X2, X3
We can also use Veda's theorem X1 + x2 + X3 = - A, x1x2x3 = - C
So x2 + X3 = - a-x1, x2x3 = - C / x1
Thus, X2 and X3 are two parts of the quadratic equation x ^ 2 + (a + x1) x-C / X1 = 0

How to solve the cubic equation of one variable? Please attach the formula and use it to solve x ^ 3 + 2x ^ 2 + 3x + 18 = 0

x=-3
Excel can be used to enter "= B1 ^ 3 + 2 * B1 ^ 2 + 3 * B1 + 18" in a cell, and enter x value in B1. Different x values can be selected according to the calculation results until the final calculation result is 0

How to solve cubic equation of one variable? Factorization is OK. Example: x ^ 3-6x ^ 2 + 3x + 10 = 0

x^3-6x^2+3x+10=0
x^2(x+1)-7x(x+1)+10(x+1)=0
（x+1）（x^2-7x+10）=0
(x+1)(x-2)(x-5)=0
x1=-1 x2=2 x3=5

Mixed operations with brackets
1. Add brackets to make the equation on the right hold: 5 × 8 + 16 △ 4-2 = 20
2. Add brackets to maximize the result of the following formula and calculate it
12+15×14+8÷4-3

5×[(8＋16)÷4-2]=20
(12+15)×(14+8)÷(4-3)=594

Find the maximum and minimum value of quadratic function y = x ^ 2 + 2 (2a-1) + 1 in the interval [1,3]

y=x^2+2(2a-1)x+1
=(x + 2a-1) ^ 2 + 1 - (2a-1) ^ 2, denoted as f (x),
1-2a ∈ [1,3], i.e. - 1

Point P is the point on the ellipse 25X ^ 2 + 9y ^ 2 = 225, and F1F2 is the focus of the ellipse, then the value of | Pf1 | + | PF2 | is ()

Solution
The elliptic equation is reduced to the standard form
(x²/3²)+(y²/5²)=1
∴a=5,b=3,c=4
It is defined by ellipse,
|PF₁|+|PF₂|=2a=10

A few simple arithmetic problems in primary school!
(160-1.5x20) divided by 0.2
(750-84x4.5) divided by 31
2.45X0.5X0.2
4.8X2.4+2.1X1.3
[Note: it's a simple operation! It's not an ordinary off form calculation! I'm online and so on 】
Division means division, because I don't know what stands for division on the keyboard 】
I want the process If I want to get the number, I can use the calculator myself

(160-1.5x20) divided by 0.2
=（130×5）÷（0.2×5）
=650
(750-84x4.5) divided by 31
=（750-378）÷31
=12
2.45X0.5X0.2
=2.45X（0.5X0.2）
=2.45X0.01
=0.0245
4.8X2.4+2.1X1.3
=11.52+2.73
=14.25

Directional derivative of function at a certain point in Higher Mathematics
I want to teach you how to calculate the directional derivative of a function in the direction of internal and external normals when solving problems like 3 and 7 in exercise 9-7 on page 108 of Volume II of mathematics of Tongji edition?

We know that the normal vector at a point on a curve or surface has two directions, the one pointing to the inside of the closed curve (surface) is the inner normal, and the one pointing to the outside of the closed curve (surface) is the outer normal

If the system of quadratic equations x + y = 4-A XY + a (x + y) = 5 has a real solution, then the value range of a is a ≥ 2 / 3 B a ≤ 2 C 2 / 3 < a < 2 D 2 / 3 < a < 2

Less than or equal to 2 / 3 and more than or equal to 2 / 3

Magic cube cfop formula letter meaning
There are some I don't know. Please send me all the possible alphabetic meanings

The letters corresponding to each face: F = front, B = back, r = right, l = left, u = up, d = down. The rotation direction and angle of each face: 90 degrees clockwise = representing letters, 90 degrees counter clockwise = representing letters ＋ "'" 180 degrees clockwise =