How to solve the quadratic equation of one variable, The more, the better

How to solve the quadratic equation of one variable, The more, the better

If the sum of the coefficients of the quadratic equation (MX + 1) (x-3) = m-2 is equal to 3, the value of M is obtained
The answer is to expand the equation, mx2-3mx + x-3 = m-2
mx2+(1-3m)x-m-1=0
That is m + 1-3m-m-1 = 3
m=-1
1. The following equations are not necessarily univariate quadratic equations are () A. (A-3) x2 = 8 (a ≠ 3) b.ax2 + BX + C = 0 C. (x + 3) (X-2) = x + 5 d. 2 in the following equations, the constant term with zero is () a.x2 + X = 1 b.2x2-x-12 = 12; C.2 (x2-1) = 3 (x-1) D.2 (x2 + 1) = x + 23. Univariate quadratic equation 2x2-3x + 1 =... Expansion
1. The following equations are not necessarily univariate quadratic equations are () A. (A-3) x2 = 8 (a ≠ 3) b.ax2 + BX + C = 0 C. (x + 3) (X-2) = x + 5 d. 2 in the following equations, the constant term with zero is () a.x2 + X = 1 b.2x2-x-12 = 12; C.2 (x2-1) = 3 (x-1) D.2 (x2 + 1) = x + 23. The univariate quadratic equation 2x2-3x + 1 = 0 is changed into the form of (x + a) 2 = B, and the correct one is () A.; B.; C.; C; D. If a root of the quadratic equation with one variable is 0, then the value is () a, B, C, or D, 5. It is known that the lengths of two sides of the triangle are 2 and 9 respectively, and the length of the third side is a root of the quadratic equation x2-14x + 48 = 0, Then the perimeter of the triangle is () a.11b.17c.17 or 19d.196. It is known that the lengths of the two right sides of a right triangle are exactly the two roots of the equation, then the lengths of the hypotenuse of the right triangle are () a, B, 3C, 6D and 97. The X that makes the value of fraction equal to zero is () a.6b. - 1 or 6C. - 1 D. If the quadratic equation ky2-4y-3 = 3Y + 4 with respect to y has real roots, Then the value range of K is () A.K > - b.k ≥ - and K ≠ 0, C.K ≥ - D.K > and K ≠ 09. Given the equation, the following statement is correct: the sum of two equations of () (a) is 1 (b), the product of two equations of () (c) is 2 (c), and the product of two equations of () (d) is 210 larger than the sum of two equations of () (a), It is known that the total turnover in the first quarter is 10 million yuan. If the average monthly growth rate is x, the equation should be () a.200 (1 + x) 2 = 1000 b.200 + 200 × 2x = 1000c.200 + 200 × 3x = 1000 d.200 [1 + (1 + x) + (1 + x) 2] = 1000]
On the problem of quadratic equation with one variable
1. The quadratic equation with X1 and X2 as roots (the coefficient of quadratic term is 1) is
2. In decomposing the factor of quadratic trinomial ax + BX + C, if the two roots of equation AX + BX + C = 0 are X1 and X2, then ax + BX + C = 0
3, the solution of quadratic equation of one variable, 4
4. It is known that the sum of the squares of the two real roots of the quadratic equation of one variable x-mx + 2m-1 = 0 is 23, and the solution of M is obtained
Ax ^ 2 + BX + C = 0A = 1, X1 + x2 = - B / a = - B, B = - (x1 + x2) x1x2 = C / a = C, C = x1x2 answer x ^ 2 - (x1 + x2) x + x1x2 = 0ax ^ 2 + BX + C = 0 www.foredu.com.cn/video/diskfile/document/2004/12/3796.pptwww.xinfanw...
2X of 6 + 1 = 1 + 3x-1 of 2
2X of 6 + 1 = 1 + 3x-1 of 2
2x/6+1=1+3x/2-1
x/3+1=3x/2
Multiply both sides by 6 at the same time
2x+6=9x
9x-2x=6
7x=6
x=6/7
(solve with equation)
1. For a project, it takes 20 hours for Party A to do it alone and 15 hours for Party B to do it alone. They started to work together. Because Party A was busy, they left for several hours. In this way, they shared 10 hours to complete the whole process. How many hours did party a leave? 2 for a project, it takes 3 days for Party A to do it alone and 5 days for Party B to do it alone. If Party A and Party B cooperate for X days to complete it, the equation can be listed_______ For a project, it takes 8 days for Party A to do it alone, 9 days for Party B to do it alone, 3 days for Party A to do it, and Party B to support it, and then x days to complete 3 / 4 of the whole project, so the equation can be drawn up____________ For a project, it takes 6 days for Party A to do it alone and 5 days for Party A and Party B to cooperate, so Party B will do the whole project every day___________ If it takes X days for B to do it alone, the equation can be given___________ And the solution is X=________ In a factory, the number of people in the first workshop is 10 more than 3 / 4 of that in the second workshop. If 30 people are transferred from the second workshop to the first workshop, the number of people in the second workshop is half of that in the first workshop____________ The equation is given__________ The original first workshop________ People, the second workshop_________ 69 workers completed 3 / 5 of a project in 14 days. Due to the need of work, if the remaining project needs to be completed in 4 days, the number of workers needs to be increased by_________ For a project, party a completed it in 10 hours, Party B in 15 hours, and Party C in 20 hours. At the beginning, the three teams cooperated. In the middle of the project, because Party A had another task, team B and team C completed it in 6 hours. How many hours did party a actually complete it? (equation solution)
1、 Shea left for X hours, and the two cooperated for 10-x hours
When a left, B did it alone. B did it alone for X hours
(1 / 20 + 1 / 15) * (10-x) is the part of cooperation between the two
Part B completed alone 1 / 15 * x
The whole project is 1, so: 1 / 15 * x + (1 / 20 + 1 / 15) * (10-x) = 1
So, x = 15, a left for 15 hours
2、 (1 / 3 + 1 / 5) * x = 1
3、 1 / 8 * 3 + (1 / 8 + 1 / 9) * x = 3 / 4
4、 B: 1 / 5-1 / 6 = 1 / 30
Equation: 1 / 6 + 1 / x = 1 / 5
5
2x-5 / 6 - 3x + 1 / 2 = 1
Solving the equation step by step
Multiply both sides by 6 at the same time
2x-5-9x-3=6
-7x=14
x=-2
Several elementary one's equation application questions
A 160m long train runs at a constant speed. First, it takes 26S to pass through tunnel a (from the front of the train to the entrance road and the rear of the train to the opening). After driving 100km, it takes 16S to pass through tunnel B and arrive at a station. The total journey is 100.352km?
A and B planes fly from two airports 750 km apart at the same time and arrive at the same Midway Airport for half an hour. If the speed of a plane is 1.5 times that of B plane, what is the speed of B plane?
The static water speed of the boat is 27 km / h, and it sails 60 km downstream to return upstream. If the water speed remains the same, the return journey takes 25% more time than downstream,
A ship, sailing between a and B, takes 3 hours to go downstream and 30 minutes more to go upstream than to go downstream,
Equation, equation
Suppose the length of tunnel a is x m, then the length of tunnel B is (100.352-100) (unit: km!) * 1000-x = (352-x), then (x + 160) / 26 = (352-x + 160) / 16, the basic formula of the problem of train crossing bridge (length of train + length of bridge) / time =
3x+(2x-1)\3=3-(x+1)\2
Multiply by 6 to get 18x + 2 (2x-1) = 18-3 (x + 1)
18x+4x-2=18-3x-3
18x+4x+3x=18-3+2
25x=17
x=17/25
The application of encounter problem
It is helpful for the responder to give an accurate answer
The two ships left from port a and port B at the same time. For the first time, the two ships met 48 km away from port B. after meeting, the two ships continued to sail. After arriving at port B and port a respectively, they immediately returned along the original road. For the second time, they met 16 km away from port B. Q: how many kilometers are there between port a and port B?
Method 1. The first meeting, two people walked a whole journey, B walked 48 kilometers, the second meeting, two people walked three whole journey, a whole journey B walked 48 kilometers, so the three whole journey B walked 48 × 3 = 144 kilometers, some time B was 16 kilometers away from B port is two whole journey, so B two ports are far away
(144 + 16) / 2 = 80 the distance between a and B is s km,
Method 2: a speed: v a speed: v b speed: V B first encounter time: H1, the second encounter time: H2, then v a × H1 / v b × h2 = v a × H2 / v b × H2
Also, the first encounter, a walked s-48 meters, that is v a × H1 = s-48, similarly, B × h2 = 48
The second time we met, B left: 2s-16, that is, v b × h2 = 2s-16, similarly, v a × h2 = S + 16
So s-48 / S = S + 16 / 2s-16
S=80
This is a bit of a problem
{x(x^2-2x+3)-3x]/1/2x^2
It's not factorization, it's computation
{x(x^2-2x+3)-3x]/1/2x^2
=(x^3-2x^2+3x-3x)/1/2x^2
=(x^3-2x^2)/1/2x^2
=2(x-2)
=2x-4
Two people along the railway line side of the trail, starting from two places, with the same speed relative to each other. A train came, the whole train from a side to drive 10 seconds. 3 minutes later, B met the train, the whole train from B side to drive only 9 seconds. The train left B______ When the two meet?
(1) Find the speed: (1 × 10 + 1 × 9) / (10-9) = 19 (M / s); (2) the distance from A3 to B3, that is, the distance between a and B when the car meets B, is also the distance between a and B: (19-1) × (10 + 190) = 3420 (m); (3) the distance from A4 to B4, that is, the distance between a and B when the car passes by B