Finding roots of cubic equation x ^ 3-3x ^ 2 + 4 = 0

Finding roots of cubic equation x ^ 3-3x ^ 2 + 4 = 0

x^3+1-3(x^2-1)
=(x+1)(x^2-x+1-3x+3)
=(x+1)(x-2)^2
So X1 = - 1, X2 = X3 = 2

Simple solution (without formula) in the root equal ratio sequence of one variable cubic equation 2x ^ 3-3x ^ 2-3x + 2 = 0

For high school stage, only one result can be observed first, which is x = - 1
So (x + 1) (2x ^ 2-5x + 2) = 0
That is, (x + 1) (2x-1) (X-2) = 0
So x = - 1, x = 1 / 2, x = 2
Hope to adopt

Let f (x) = x ^ 3 + 4x ^ 2-3x-1, and try to discuss the real roots of the equation f (x) = 0 in the interval from negative infinity to zero

From F '(x) = 3x ^ 2 + 8x-3 = (3x-1) (x + 3) = 0, the extreme point x = - 3, 1 / 3 is obtained
Maximum f (- 3) = - 27 + 36 + 27-1 = 35 > 0
Minimum f (1 / 3) = 1 / 27 + 4 / 9-1-1

1. It is known that the square of B minus 4ac is the root of the equation a times x plus BX plus C = 0, and the value of AB (a is not equal to 0) can be obtained

1/8

Can the multiplication sign be omitted when multiplying integers and fractions? If so, how can it be distinguished from fractions? Or under what circumstances can it be saved?
If 6 is followed by 25 / 9 of the root, does it represent multiplication by

It can not be omitted, only when it is multiplied by the unknown

The pronunciation of "number"
Yanzi said, "zhuzou is guilty of three crimes. Please count them and kill them with their crimes." Gonghe said, "yes." so he called zhuzou and said, "zhuzou, it's a crime to kill you for my king's bird. It's a crime to kill you for my king's bird. It's a crime to kill you for my king's bird. It's a crime to make princes hear about it, and it's a crime to despise people for my king's bird.", Please kill it. The duke said, "don't kill me. I don't know my life."
"Number" in "please count" means enumeration, so what does it read?

3

Simple, don't tell me to use the formula of distance from point to line

The straight line y = KX + B, the slope is k, and the known point is a (a, b)
Let the symmetric point be p (x, y), then the coordinates of the midpoint of AP are x '= (x + a) / 2, y' = (y + b), which must be on y = KX + B, and then a equation (1) is obtained
If AP is perpendicular to y = KX + B, then the slope of AP = - 1 / K, that is, (y-b) / (x-a) = - 1 / K, (2)
(1) (2) get the P coordinate

Solving 60 written decimal problems in Volume 2 of grade 4

Finding the number of real roots of equation LG (x + 4) = - 10 ^ x

1

Find the area of the inscribed square of the ellipse e: X & # 178 / / A & # 178; + Y & # 178 / / B & # 178; = 1 (A & gt; B & gt; 0)