It is known that the two intersections of parabola y = - x ^ 2 + BX + C and X axis are a (m, 0) B (n, 0), and N + M = 4, M / N = 1 / 3 Find the analytic expression of this function

It is known that the two intersections of parabola y = - x ^ 2 + BX + C and X axis are a (m, 0) B (n, 0), and N + M = 4, M / N = 1 / 3 Find the analytic expression of this function

n. M is the two roots of the equation - x ^ 2 + BX + C = 0,
X ^ 2-bx-c = 0
n+m=4,m/n=1/3
n=3m
m=1
N = 3 by Weida theorem
n+m=b=4
nm=-c=3
c=-3
y=-x^2+4x-3

It is known that the parabola y = ax & # 178; + BX + C (a ≠ 0, a ≠ C) passes through the point a (1,0), the vertex is B, and the parabola does not pass through the third quadrant
(2) Judge the quadrant of point B and explain the reason
(3) If the straight line y2 = 2x + m passes through point B and intersects with the parabola at another point C (C / A, B + 8), the value range of Y1 is obtained when x ≥ 1

Over a (1,0), then 0 = a + B + C, B = - (a + C)
But in the third quadrant, a > 0, C > = 0, so B0
y=(4ac-b²)/4a=(4ac-(a+c)^2)/4a=-(a-c)^2/4a

2.9.12.23.39.111.1001.92.285.98. Who are the even number, the odd number, the prime number and the composite number

Even numbers are 2,12,92,98, and the rest are odd numbers. Prime numbers are 2,231001, and the rest are composite numbers

About 2 (X-Y) ^ 3 / (Y-X)

2（x-y）^3/(y-x)
=-2（x-y）^3/(x-y)
=-2(x-y)²

(x + y) ^ 2 (X-Y) + (x + y) (Y-X) ^ 2 to extract the common factor

(x+y)^2(x-y)+(x+y)(y-x)^2
=(x+y)^2(x-y)+(x+y)(x-y)^2
=(x+y(x-y)[(x+y)+(x-y)]
=(x+y(x-y)(x+y+x-y)
=2x(x+y)(x-y)

Given X & sup2; - 2xy-3y & sup2; = 0, x > 0, Y > 0, find the value of X + 2Y of X-Y

x²-2xy-3y²=0
(x-3y)(x+y)=0
x> If Y > 0, then x + y ≠ 0
So x-3y = 0
x=3y
So the original formula = (3y-y) 3Y + 2Y)
=5Y out of 2Y
=5 / 2

A problem of one variable linear equation in grade one
1. No matter what the value of X is, the identity of the equation AX + b-4x = 3 holds, and the value of A.B is obtained

(a-4)x=3-b
Let X be any value
You need both left and right expressions to be 0
So a = 4; b = 3

How to find the unknowns in the quadratic equation of two variables

Elimination

It is known that the fourth power of polynomial x + the second power of 2012x + 2011x + 2012 has a factor of the second power of X + ax + 1, and the other is the second power of X + BX + 2012 to find a + B

The factorization of the fourth power of X + the second power of 2012x + 2011x + 2012 is (X & # 178; + ax + 1) (X & # 178; + BX + 2012)
So the cubic coefficient is 0
So a + B = 0 -------- a + B is the cubic coefficient

Let u = {0,1,2,3}. A = {x ∈ u | x + MX = 0}. If CUA = {1,2}, what is the real number m?

∵CuA={1,2}.
∴A={0、3}
0 + 0m = 0 and 3 + 3M = 0
∴m=-1