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

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

Truth. The converse proposition is the same as the original proposition
If M > 1 / 4, then 1-4m is less than zero, which is equivalent to the quadratic equation MX & # 178; - x + 1 = 0 has no real root

If the intersection point of parabola y = 49 (x − 3) 2 and X axis is a, and the intersection point of parabola y = 49 (x − 3) 2 and Y axis is B, then the area of △ AOB is______ ．

∵ the intersection of y = 49 (x − 3) 2 and X axis is a, the intersection of Y axis and Y axis is B, ∵ 0 = 49 (x − 3) 2, the solution is: x = 3, when x = 0, y = 4, ∵ a (3,0), B (0,4), ∵ AOB area is: 12 × 3 × 4 = 6

The coordinates of two intersections of parabola y = x & # 178; - 1999x + 2000 and X axis are (a, 0) (B, 0)
Find the value of (A & # 178; - 2000a + 2000) (B & # 178; - 2000b + 2000)
A -1999 B.-2000 C.1999 D 2000

Choose D! From the problem meaning a, B are the two solutions of the equation x ^ 2-1999x + 2000 = 0, so bring in the equation to get a & # 178; - 1999a + 2000 = 0; B & # 178; - 1999b + 2000 = 0; then the original formula = (0-A) (0-B) = AB; according to the relationship between the root and coefficient, ab = 2000, so the original formula = 2000, so choose D. tips: use the root and the coefficient flexibly

The coordinates of the intersection of the parabola y = 4 (X-2) 2 and the Y axis are______ ．

∵ y = 4 (X-2) 2, ∵ when x = 0, y = 16, ∵ the intersection coordinates of parabolic y = 4 (X-2) 2 and Y axis are (0, 16). So the answer is: (0, 16)