It is known that X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1 It is known that X1 and X2 are two real number roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1. Is there a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2? If so, find the value of K. if not, explain the reason. 2. Find the integer value of the real number k with the value of X1 / x2 + x2 / x1-2 as an integer

It is known that X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1 It is known that X1 and X2 are two real number roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1. Is there a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2? If so, find the value of K. if not, explain the reason. 2. Find the integer value of the real number k with the value of X1 / x2 + x2 / x1-2 as an integer

From the problem, we know that X1 + x2 = 1, X1 * x2 = 1 / 4K, (2x1-x2) (x1-2x2) = 2x1 ^ 2-5x1 * x2 + 2x2 ^ 2 = 2 (x1 + x2) ^ 2-9x1 * x2 = 2-9 / 4K = - 3 / 2, we get k = 9 / 14. From the problem, we know that the quadratic equation with one variable has two real roots, and we get 16K ^ 2-16k > 0, k > 1 or k > 1

It is known that X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1. Whether there is a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2 holds
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It is known that X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0. 1. Is there a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2 holds? If it exists, find the value of K. If not. Please give reasons. 2. Find the integer value of the real number k that makes the value of X1 / x2 + x2 / x1-2 an integer.

1. X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + 1 = 0
Ψ△ = (- 4K) ^ 2-16k ≥ 0, K (k-1) ≥ 0, K ≥ 1 or K ≤ 0
Suppose there is a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2 holds, then
（2x1-x2）(x1-2x2)=2(x1)^2+2(x2)^2-5x1x2=2(x1+x2)^2-9x1x2
∵x1+x2=1 x1x2=1/(4k)
∴（2x1-x2）(x1-2x2)=2-9/(4k)=-3/2 ∴k=9/14
And K ≥ 1 or K ≤ 0
There is no real number k such that (2x1-x2) (x1-2x2) = - 3 / 2 holds
2、x1/x2+x2/x1-2=[(x1)^2+(x2)^2]/(x1x2)-2=[(x1+x2)^2-2x1x2]/(x1x2)-2
=[1-1/(2k)]*(4k)-2=4k-4
Make the value of X1 / x2 + x2 / x1-2 an integer, even if the value of 4k-4 is an integer
‖ K is an integer

It is known that X1 and X2 are two real roots of the quadratic equation 4kx ^ 2-4kx + K + 1 = 0 with respect to X
(1) Is there a real number k such that (2x1-x2) (x1-2x2) = - 3 / 2 holds? If so, find the value of K. if not, explain the reason
(2) Find the integer value of the real number k with the value of (x1 / x2) + (x2 / x1) - 2 as an integer
(3) If k = - 2, α = X1 / X2, try to find the value of α

Then: X1 + x2 = - (- 4K) / 4K = 1x1x2 = (K + 1) / 4k1) (2x1-x2) (x1-2x) = 2x1 ^ 2 + 2x2 ^ 2-5x1x2 = 2 (x1 + x2) ^ 2-9x1x2 = 2-9 (K + 1) / 4K = - 3 / 29 (K + 1) / 4K = 7 / 29 (K + 1) = 14kk = 9 / 52) X1 / x2 + x2 / x1-2 = (x1 ^ 2 + x2 ^

Given that X1 and X2 are two real roots of the quadratic equation 4kx2-4kx + K + 1 = 0, then the integer value of the real number k with the value of x1x2 + x2x1 − 2 as an integer is______ ．

∵ x1, X2 are two real roots of the quadratic equation of one variable 4kx2-4kx + K + 1 = 0, ∵ X1 + x2 = 1, x1x2 = K + 14K, ∵ x1x2 + x2x1-2 = X12 + x22x1x2-2 = (x1 + x2) 2 − 2x1x2x1x2-2 = 1 − K + 12kk + 14k-2 = 2K − 2K + 1-2 = − 4K + 1

For the quadratic equation kx2 - (2k + 1) x + k = 0 with one variable of X, if there are two real roots, then the value range of K is ()
A. K ＞ - 14b. K ≥ - 14C. K ＜ - 14 and K ≠ 0d. K ≥ - 14 and K ≠ 0

∵△ = b2-4ac = (2k + 1) 2-4k2 ≥ 0, the solution is k ≥ - 14, and the quadratic coefficient K ≠ 0, ∵ K ≥ - 14 and K ≠ 0

Algebraic formula, practical problems and quadratic equation of one variable (2 problems in total) are troublesome to solve,
1. If x ≠ y and satisfy the equations X & sup2; + 2x-5 = 0 and Y & sup2; + 2y-5 = 0, what is 1 / x + 1 / y equal to?
2. On a 92 m long and 62 m wide rectangular cultivated land, three canals with the same width shall be excavated, one of which shall be parallel to the bottom edge and the other two shall be perpendicular to the bottom edge. The cultivated land shall be divided into small rectangular pieces with an area of 885 M & sup2; by canals. How wide shall the rectangle be excavated? (only the formula is required)

1. X and y are two different roots of the equation x & sup2; + 2x-5 = 0,
So: x + y = - 2, xy = - 5, so the formula is 2 / 5
2. Let the moment width be B
Equation 1: 885 * 6 + (92 + 2 * 62) * b-2b ^ 2 = 92 * 62

If you want to solve the quadratic equation with one variable, if you want the equation and the result, you'd better give me the answer on the same day
1. A store bought a batch of sportswear for 10000 yuan, and each set was sold for 100 yuan. If all the sportswear were sold, the difference between the money obtained from this batch of sportswear and the money used to buy this batch of sportswear is the profit. According to this calculation, the profit obtained from this sale is just the money used to buy 11 sportswear. How many sets of sportswear are there?
2. A farm plans to build a channel with isosceles trapezoid cross section, with a cross section area of 0.65 square meters. The width of the upper entrance is 1.4m more than the width of the channel bottom, and the depth of the channel is 0.1M less than the width of the channel bottom. What is the width of the channel bottom?
3. A city enrolled 50 junior and middle school students in the province in September 2006, and plans to end the enrollment in September 2008, so that the number of junior middle school students in the province will reach 450. If the average annual growth rate of junior middle school students in the city is the same as that of the previous year, what is the growth rate?
4. After two price cuts, the price of a batch of TV sets has been reduced from 2250 yuan per set to 1440 yuan per set. What is the average percentage of each price cut?
5. A two digit number is equal to the square of the number on its one digit. The number on its one digit is three times larger than that on its ten digit number. What is the two digit number?
6. A product plans to reduce its cost by 36% in two years. What is the average annual reduction percentage?
7. If the two engineering teams of Party A and Party B complete a certain project, if the two teams start work at the same time, the project can be completed in 12 days. It takes 10 more days for Party B to complete the project alone than for Party A. how many days does it take for Party B to complete the project alone?
8. On New Year's day, each student of an interest group in a class presents a new year's card to the rest of the students. In this way, the class gives each other 56 new year's cards. How many people are there in this interest group?
School is about to start,

Please forgive me for not asking for answers
(1) Suppose there are x sets of these sportswear
100X-10000=11*10000/X
X(100X-10000)=110000
(2) Let the width of the canal bottom be x meters
（1.4+2X）（X-0.1）=0.65
(3) Let the growth rate be X
50（1+X）²=450
(4) Let X be the average percentage of each reduction
2250（1-X）²=1440
(5) Set the number of digits to X
10（X-3）+X=X²
(6) Let the average annual decrease be X
（1-X）²=36%
(7) It takes X days to set up team B alone
1÷（1/X+1/（X-10））=12
X(X-10)=24X-120
(8) There are x people in this interest group
X(X-1)=56

When what is the value, the equation about (1) has two unequal real roots; (2) has two equal real roots; (3) has no real roots
x²-（2k-1）x=-k²+2k+3

When △ 0, there are two unequal real roots
When △ = 0, there are two unequal real roots
When △ 0, there are two unequal real roots
△＝b²-4ac
Do it yourself

It is known that the quadratic equation of one variable x2-4x + k = 0 has two unequal real roots, and the equation has the same root as x2 + MX-1 = 0. When k is the largest integer that meets the condition, the value of M is... The answer is 0 or - 3 / 8, why not omit the latter? In formula 2, from b2-4ac greater than or equal to 0, we can get that M greater than is equal to plus or minus 2,

You're wrong
In formula 2, b2-4ac is greater than or equal to 0:
Namely
m^2+4>=0
That is to say, any m satisfies this formula

Discriminant of quadratic equation with one variable
On the discriminant △ of the roots of the quadratic equation AX ^ 2 + BX + C = 0 (a ≠ 0)=_____
(1) When △ 0, the root of ax ^ 2 + BX + C = 0 (a ≠ 0) is______
(2) When △ = 0, the root of ax ^ 2 + BX + C = 0 (a ≠ 0) is______
(3) When △ 0, the root of ax ^ 2 + BX + C = 0 (a ≠ 0) is______

Discriminant = B ^ 2-4ac
1) 2 A-B plus (minus) radical B ^ 2-4ac
2) The - B of 2A plus (or minus) radical B ^ 2-4ac
3) No solution