Factorization of quadratic function s ^ 2 + S + 1 with discriminant less than 0

Factorization of quadratic function s ^ 2 + S + 1 with discriminant less than 0

s^2+s+1
=(s+1/2)^2+3/4
=(s+1/2+√3i/2)(s+1/2-√3i/2)

Why is it necessary to factorize if △ = complete square?
What about △ 0? Can't it be factorized? What's the relationship between them

If △ = 0, the root of quadratic equation is rational number, which can be factorized in junior high school. If △ > 0, the root of quadratic equation can be irrational number, which cannot be factorized in junior high school

The three views of a geometry are shown in the figure. The main view and top view are rectangles. If the left view is a right triangle, its surface area is ()

First of all, we can judge that it is a triangular prism. Suppose that the side length = a. the surface area = A2 + A2 + 2 * 1 / 2 * A2 + 2 / 2A2 = 3a2
+2 root 2

As shown in the figure is a side expansion of a solid figure, calculate its total area and volume

(1) Its total area is: 14 × (3.14 × 102 × 2 + 3.14 × 2 × 10 × 8) + 10 × 8 × 2, = 14 × (628 + 502.4) + 160, = 14 × 1130.4 + 160, = 282.6 + 160, = 442.6 (square centimeter), (2) its volume is: 14 × 3.14 × 102 × 8 = 628 (cubic centimeter)

How many cubic meters is a ton of stone!

The density of various rocks and sands is too different. For example, the density of granite and volcanic rocks is several times different! Even if someone answers your question, the error of the data will be great!
The average specific gravity of stone is 2.7 tons per cubic meter

Solving equation 7200 / x-7200-7200 (1 + 20%) / x = 4
The second formula is that the numerator is 7200 (1 + 20%) and the denominator is X

7200*（1/x-1-1.2/x)=4
-0.2/x-1=1/1800
x=-0.2/(1+1/1800)=-1800/9005

Given that the image of parabola y = - x ^ 2 + 4x-3 intersects Y axis at point B and X axis at two points AC, the area of △ ABC can be calculated

Intersection B (0, - 3) with y axis, two intersections X1 + x2 = - 2, X1 * x2 = - 3, | x1-x2 | = 4, area s = 6 with X axis

What is the relationship between density and severity?

m=rv

There are two old people with white hair sitting in the park. Next to them are two young people. The old man said, "the square difference of our two ages is 195..." (to be continued)
There are two old people with white hair sitting in the park. Next to them are two young people. The old man said, "the square difference of our two ages is 195..." Young people love happily said: "I and her age square difference is 195." at this time, a middle-aged couple came to say: "our age square difference is 195."
Now, please think about it. What's the age of the three couples? In fact, there are four couples whose square difference is 195. You might as well find out the four couples~
It's not just the answer, it's the process

The age of two old people: 98,97;
The age of two young people: 22,17;
The age of two middle-aged people: 34,31;
The fourth possible age combination is 14 years old and 1 year old;
The algorithm is very simple. The square difference of the two ages is 195, that is, (a + b) (a-b) = 195;
It is a multiplication relation, so we first require 195 to be a common divisor (that is, 195 / (a + b) must be an integer), and it is easy to know that 195 has four common divisors: 1; 3; 5; 13,
So we have the formula:
(1) (a-b) = 1 (a + b) = 195 / 1 = 195, a = 98; b = 97
(2) (a-b) = 3 (a + b) = 195 / 3 = 65, a = 34; b = 31
(3) (a-b) = 5 (a + b) = 195 / 5 = 39, a = 22; b = 17
(4) (a-b) = 13 (a + b) = 195 / 13 = 15, a = 14; b = 1

It is known that the focal point of the parabola y2 = 4x is f and the directrix is L. if the intersection of the straight line passing through the point F with an inclination angle of 60 ° and the parabola in the first quadrant is a, and the perpendicular line passing through a is l and the perpendicular foot is A1, then the area of △ aa1f is______ ．

From the known conditions, the parabolic directrix is x = - 1, the focus is (1, 0), and the inclination angle of the straight line is 60 °, the slope k = Tan 60 ° = 3 is obtained. Let the straight line equation with the inclination angle of 60 ° through point F be y = 3 (x-1). Substituting it into the parabolic equation, we can get 3 (x-1) 2 = 4x ｛ 3x2-10x + 3 = 0 ｛ x = 3, or x = 13 ｛ a in the first quadrant ｛ a point coordinate (3, 23) ｛ Aa1 ﹤ 4 ｛ s △ aa1f = 12 × 4 × 23 = 43, so the answer is: 43