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On the univariate quadratic equation of X (m-1) x2 + (2m + 1) x + M2-1 = 0, then the value of M is 0______ ．
Substituting x = 0 into the equation: M2-1 = 0, M-1 ≠ 0, the solution: M = - 1
When the value of M is in what range, the univariate quadratic equation mx2-4x + 5 = 0 and x2-4mx + 4m2-3m-3 = 0 have real roots. Is there an integer m such that the roots of the equation are also integers? If it exists, request; if it does not exist, please explain the reason
∵ the univariate quadratic equation mx2-4x + 5 = 0 and x2-4mx + 4m2-3m-3 = 0 have real roots, m ≠ 016 − 20m ≥ 016m2 − 4 (4m2 − 3M − 3) ≥ 0, the solution is - 1 ≤ m ≤ 45 and m ≠ 0, that is, when - 1 ≤ m ≤ 45 and m ≠ 0, the univariate quadratic equation mx2-4x + 5 = 0 and x2-4mx + 4m2-3m-3 = 0 have real roots 2-4x + 5 = 0 is - x2-4x + 5 = 0, the solution is X1 = - 5, X2 = 1, which is consistent with the meaning of the problem; when m = - 1, the equation x2-4mx + 4m2-3m-3 = 0 is x2 + 4x + 4 = 0, the solution is X1 = x2 = - 2, which is consistent with the meaning of the problem; therefore, there is an integer m = - 1, so that the root of the equation is also an integer
It is known that the focus of line L passing through line 3x + 4Y-2 = 0 and line 2x + y + 2 = 0 is p, and it is perpendicular to line x-2y-1 = 0
The equation for finding the line L
Find the area of L and axis besieged city!
1.
The intersection of 3x + 4Y-2 = 0 and 2x + y + 2 = 0 is p (- 2,2)
Because perpendicular to the line x-2y-1 = 0, the slope is - 2
The equation is Y-2 = - 2 (x + 2), that is, 2x + y + 2 = 0
two
The intersection of L and coordinate axis is (- 1,0), (0, - 2)
So the area is 1
The equations are solved by substitution elimination method and addition and subtraction elimination method respectively: x + y = 7, 3x + 5Y = 17
Two methods were used
X + y = 7, 1 3x + 5Y = 17, 2 2x + 3Y = 21, 2 - 3 2Y = - 4Y = - 2, substituting y = - 2 into 1 to get x = 9, so x = 9y = - 2x + y = 7, 1 3x + 5Y = 17, 2 from 1 to get y = 7-x, 3 from 1 to get 3x + 35-5x = 17-2x = - 18x = 9, substituting x = 9 into 3 to get y = - 2, so x = 9y
RELATED INFORMATIONS
- 1. To solve the equations, one half x + one third y = 1 3x-y = 2
- 2. Judge the truth of the converse proposition of "if M > 0, then equation x2 + 2x-3m = 0 has real root"
- 3. Judge whether the inverse proposition of the proposition "if M > 1 / 4, then the quadratic equation MX & # 178; - x + 1 = 0 has no real root" is true or false
- 4. Find the area of the intersection coordinates a, B and △ AOB of the straight line y = 2x + 8 and the parabola y = x & # 178
- 5. The intersection of the line y = x and the parabola y = - 2x2 is () A. （12，0）B. （-12，-12）C. （-12，-12），（0，0）D. （0，0）
- 6. The number of intersections of parabola y = - 3 ^ 2 + 2x-1 and coordinate axis is () A. 0 B. 1 C. 2 D. 3
- 7. How many intersections are there between the parabola y = x ^ 2-ax + A-2 and the coordinate axis I really think it's three, but the teacher said no, she said three wrong, help me!
- 8. It is known that the parabola y = MX & sup2; + (M-6) X-6 (the constant M is not equal to 0) (1) when m is the value, the distance between the two intersections of the parabola and the X axis is equal to 2 When I set up the equation, the answer is always wrong
- 9. Given that the square of the parabolic equation y = MX (M belongs to R, and M is not equal to 0) 1, if the focal coordinate of the parabola is (1,0), the equation of the parabola is solved
- 10. It is known that there is only one intersection point C between the parabola and the x-axis, and it intersects with the straight line y = x + 2 at two points AB, where a is on the y-axis AC = 2 root 2 (1) to find the analytical formula of the parabola（ It is known that there is only one intersection point C between the parabola and the y-axis, and the parabola and the straight line y = x + 2 intersect at two points AB, where a on the y-axis AC = 2 root sign 2 (1) find the analytical formula of the parabola (2) if point B is on the right side of point a, P is a point on the line AB (point P and ab do not coincide with each other, passing through point P to make the vertical angle of the x-axis parabola at Q. suppose that the length of PQ is MP and the abscissa is x, find the functional relationship between M and x, and write out the value range of the independent variable x (3) Whether there is a point P on the line AB so that the circle with the diameter of the line PQ in 2 passes through the point A. if there is, the coordinates of the point P can be obtained There should be only one intersection point C with the X axis
- 11. It is known that the integer m satisfies 6 ＜ m ＜ 20. If the quadratic equation MX2 - (2m-1) x + m-2 = 0 with respect to X has a rational root, the value of M and the root of the equation are obtained
- 12. Given the set a = {x | X & # 178; + ax + B = 0} = {1,2}, (1) find the value of a, B, (2) inequality | 2x-a|
- 13. If the result of inequality 1 / 3 (2x-k) > x-k is X There's another one Given that the solutions X and y of the equations y-2x = m (1), 2Y + 3x = m + 1 (2) satisfy 2x + y ≥ 0, the value range of M is obtained.
- 14. Finding inequality 3 (x + 1) greater than or equal to 5x-9
- 15. 0.4x ≤ - 0.84 solution inequality
- 16. Solve the inequality: 5x > 3 (x-3) + 2,4 of X + 4-6 of X-1 < 1, X-2 of X-1, ≥ 2-3 of X + 2
- 17. Solving inequality (x + 2) (x-3)
- 18. Finding the integer solution of inequality {x-3 (X-2) ≥ 4, (1 + 4x) / 3 > X-1
- 19. Why write solutions when solving equations
- 20. 36 red balls and 24 yellow balls, the same size, are packed in the same kind of box, each kind of ball is just finished, how many can each box hold at most? How many boxes do you need?