1. We know the equation x & # 178; + 2kx + k-1 = 0 (1) To prove that the equation has two unequal real roots (2) When k is the value, the two parts of the equation are opposite to each other 2. It is known that X & # 8321;, X & # 8322; are two non-zero real number roots of the quadratic equation 4x & # 178; + 4 (m-1) x + M & # 178; = 0 about X. can X & # 8321; and X & # 8322; have the same sign? If they can have the same sign, ask for the corresponding value range of M; if not, explain the reason

1. (1) (2k) & # 178; - 4 (k-1) = 4K & # 178; - 4K + 4 = 4 (k-1 / 2) & # 178; + 3 because (k-1 / 2) & # 178; ≥ 0, so 4 (k-1 / 2) & # 178; + 3 is always greater than 0, that is to say, the equation has two unequal roots of real numbers (2) and two opposite numbers, then X1 + x2 = - 2K = 0, k = 0 is substituted into X & # 178; - 1 = 0, x = ± 1 satisfies the meaning of the problem
x²＋2kx＋k－1=0
1. Discriminant = (2k) &# 178; - 4 (k-1) = 4K & # 178; - 4K + 4 = 4 (K & # 178; - K + 1)
Because K & # 178; - K + 1 = [K - (1 / 2)] &# 178; + (3 / 4) > 0
So this equation has two unequal real roots.
2. If two numbers are opposite to each other, then X1 + x2 = 0, then 2K = 0, then k = 0
In this case, the equation is: X & # 178; - 1 = 0
x²＋2kx＋k－1=0
1. Discriminant = (2k) &# 178; - 4 (k-1) = 4K & # 178; - 4K + 4 = 4 (K & # 178; - K + 1)
Because K & # 178; - K + 1 = [K - (1 / 2)] &# 178; + (3 / 4) > 0
So this equation has two unequal real roots.
2. If two numbers are opposite to each other, then X1 + x2 = 0, then 2K = 0, then k = 0
In this case, the equation is: X & # 178; - 1 = 0, then: X1 = 1, X2 = - 1
Two
For the same number, x1x2 > 0
That is, x1x2 = M & # / 4 > 0
m²>0
m≠0
The discriminant is greater than or equal to 0
16(m-1)²-16m²>=0
-2m+1>=0
M0
So: the equation has two unequal real roots.
1.2) two numbers are opposite to each other
x1+x2=-2k=0，k=0
So: when two numbers are opposite to each other, k = 0
(2) X1 and X2 are two nonzero real roots of the equation 4x & # 178; + 4 (m-1) x + M & # 178; = 0. When two of them have the same sign, the product is greater than 0
According to Weida's theorem: X1 * x2 = M & # 178 / 4 > 0, m ≠ 0
The discriminant = 16 (m-1) &# 178; - 4 * 4 * M & # 178; > = 0, that is: - 2m + 1 > = 0, M
Try to judge the case of equation (k-1) x & # 178; + 2kx + K + 3 = 0 root about X
Discriminant
(2k)²-4x(K+3)x(k-1)
=4k²-4(k²+2k-3)
=4k²-4k²-8k+12
=12-8k
k> There is no real root at 3 / 2
When k = 3 / 2 and 1, there is a real root
K
Given that x = 1 is a root of the equation 2kx & # 178; + KX + 2 = K & # 178; (k > 0) about X, find the root of another equation y & # 178; - 4ky + 15 = 0
k≥0
By substituting x = 1 into the equation 2kx & # 178; + KX + 2 = K & # 178;, 2K + K + 2 = K & # 178;, K & # 178; - 3K-2 = 0. Because k > 0, k = (3-radical 17) / 2. In this way, the second equation is not easy to solve. I think x = - 1 is the solution. Then the equation about K is: K & # 178; - K-2 = 0, because k > 0, k = - 1. Y &
Reference content: above
Eight matches make up a fish figure. You can only move three matches to make the whole fish figure in the opposite direction. How can you move it?
Number matches from top to bottom, left to right, 1, 2, 3, 4, 5, 6, 7, 8
Take down No. 2 and No. 4 in proper position
One at the intersection of 5, 6, 8
One between seven and eight
One under number eight
That's it
Examples of converting internal energy into electrical energy
I think it's right on the second floor, but I don't know
When two different metals are bonded together and heated, electricity is generated,
The first floor is chemical energy into internal energy, internal energy into mechanical energy, mechanical energy into electrical energy
How much horsepower is 110 kW
1 horsepower is about 735 watts, how much is the specific equivalent? It is suggested to check Baidu, and then calculate by yourself
The order of four mixed operations,
Multiply and divide first, then add and subtract,
First do multiplication and division, and finally do addition and subtraction. When doing multiplication and division, we must follow the order from left to right
Move only three of the eight matches to make the fish move in the opposite direction
Four for fish body, two for fish tail. Main: and two for shark fin
Number matches from top to bottom, left to right, 1, 2, 3, 4, 5, 6, 7, 8
Take down No. 1, No. 2 and No. 4 and put them in a suitable position:
One at the intersection of 5, 6, 8
One between seven and eight
One under number eight
That's it
What kind of energy can electric energy be converted into? Please give an example
Conversion of electric energy into heat energy: electric furnace
Conversion of electric energy into light energy: when an electric lamp lights, it converts electric energy into light energy and internal energy
Conversion of electrical energy into chemical energy: Batteries
Electrical energy into mechanical energy: motors, fans
Light energy (electric lamp) internal energy (electric heater) mechanical energy (motor)
Energy, potential energy, kinetic energy, mechanical energy
Convert into kinetic energy, such as electric motor, into heat energy, such as heater, into magnetic energy, such as electromagnet, into light energy, such as electric lamp
How many kW is one horsepower equal to
But this kind of regulation has certain basis
There is no formula!
I hope it's useful to you! Question: what's 1 horsepower equal to? Nm answer: nm (nm) is a unit of torque. Horsepower is not a force, but a unit of power
The power is calculated by torque, and the calculation formula is quite simple: power (W) = 2 π × torque (n-m) × speed (RPM) / 60. After simplified calculation, it becomes: power (kw) = torque (n-m) × speed (RPM) / 9549

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