The equation x ^ 2 + 2x + a = 0 of X has a solution in the interval [- 3,1]. Find the value range of real number a

Firstly, because the equation x ^ 2 + 2x + a = 0 about X has a solution in the interval [- 3,1], the discriminant is nonnegative, that is, 4-4a > = 0
The solution is a

Given that the equation x ^ 2-2x-3 + a = 0 has and only has one root on [0,4], we can find the range of real number a

x^2-2x-3+a=0
y=x^2-2x-3+a=(x-1)^2+a-4
The axis of symmetry is x = 1, opening up!
1) It has the same two roots
x=1 y=0
a=4
2) There are two unequal real roots
Discriminant > 0
f(0)*f(4)0
(a-3)*(a+5)

How to transform polar coordinate equation into rectangular coordinate equation

The following formula can be used:
ρ²=x²+y²
ρcosθ=x
ρsinθ=y

A batch of cement was required to be transported in three days. 114 tons were transported in the first day, and the remaining 2 / 7 were transported in the second day. Half of this batch of cement was transported in the third day
How many tons of cement are left after the first day of transportation

Lucky in the first two days = lucky in the third day
So 114 / [(1-2 / 7) - 2 / 7] = 266 tons

Let OA = (3,1), OB = (- 1,2), OC be perpendicular to ob, BC be parallel to OA, and then calculate OC

Let OC (x, y) BC = Bo + OC = (1, - 2) + (x, y) = (1 + X, Y-2)
By OC * ob = - x + 2Y = 0, by BC parallel OA, then (1 + x) / 3 = (Y-2) / 1
The solution is x = 14, y = 7, so the vector OC = (14,7)

For a pile of 30 tons of yellow sand, one fifth of the total amount will be used in the first time, and five quarters of the amount will be used in the second time. How many tons of yellow sand will be used in the second time?

30 times 1 / 5 to get 6 tons for the first time, then 6 times 5 / 4 to get 7.5 tons

Find the maximum value of the function y = Log1 / 5 (X & sup2; - 6x + 10) in the interval [1,2]
What is the maximum value? Is there a specific value?

x^2-6x+10
=(x-3)^2+1
Monotone decreasing on interval [1,2]
The minimum value is 2, where x = 2
Because log (1 / 5) x is monotonically decreasing
So y = Log1 / 5 (x ^ 2-6x + 10)

A company had 310 employees last year. After the layoffs, the number of male employees decreased by 30 and female employees by 20%. The total number of employees decreased by 56. How many female employees are there now?

104

Factorization of (XY) & - 4
Factorization
1：(xy)²-4
2：16a²-（2b）²
3：-9+25x²

1：(xy)²-4=(xy+2)(xy-2)
2：16a²-（2b）²=（4a-2b）（4a+2b）
3：-9+25x²=(5x-3)(5x+3)

There are 128 students in the sixth grade of a primary school. 62.5% of them have reached the standard of physical exercise, and 40% of them are girls. What percentage of the total number of boys who have reached the standard in six years? 2. Wangjiang township has planted 230 hectares of trees this spring, which is more than 15% of the plan. How many hectares of trees were planned? 3. A clothing store has sold a piece of clothes at a discount of 10%, and the original price of the clothes is 300 yuan, making a profit of 40 yuan, After the discount, then (). (profit or loss? How much profit, how much loss?)

1. 62.5% × (1-40%) = 37.5%, so the number of boys reaching the standard accounts for 37.5% of the total number in six years
2. 230 ÷ (1 + 15%) = 200, so it was planned to afforest 200 hectares
3. 300 × 9 / 10 = 270 yuan
300-40 = 260 yuan
270-260 = 10 yuan
So after the discount can still profit, profit 10 yuan

The equation x ^ 2 + 2x + a = 0 of X has a solution in the interval [- 3,1]. Find the value range of real number a