On quadratic equation of one variable 1. It is known that m.n is the equation x2-2008x + 2009 = 0 about X, which has two real roots. Find the value of the algebraic formula (m2-2008m + 2009) 2. When finding the value of real number k, the quadratic equation X2 - (2k-3) x + 2k-4 = 0 has two positive roots 3. It is known that there are two negative roots of quadratic equation 6x2 + (M + 1) x + m-5 = 0, so we can find the value range of real number M Note: 2 after each unknown is the square I haven't thought about it for a long time. Who can accompany me to have a look

On quadratic equation of one variable 1. It is known that m.n is the equation x2-2008x + 2009 = 0 about X, which has two real roots. Find the value of the algebraic formula (m2-2008m + 2009) 2. When finding the value of real number k, the quadratic equation X2 - (2k-3) x + 2k-4 = 0 has two positive roots 3. It is known that there are two negative roots of quadratic equation 6x2 + (M + 1) x + m-5 = 0, so we can find the value range of real number M Note: 2 after each unknown is the square I haven't thought about it for a long time. Who can accompany me to have a look

1. According to the relationship between root and coefficient, it can be concluded that
M*N=C/A
M+N=-B/A
That is m * n = 2009
M+N=2008
Take this result to the second equation
M2 - (M + n) m + (m * n) is obtained
It's 0 at the end
2. Similarly (question 3)
X1*X2=2K-4
2K-4>0 K>2 X1+X2=2K-3
2k-3 > 0, k > 1.5
So k > 2
3. Because both of them are negative, X1 * x2 = (m-5) / 6 is positive with the same sign
（M-5)/6>0 M>5 X1+X2=-M+1/6 ,-M+1/6-1
So m > 5
My humble opinion is for reference only

A mathematical problem of grade two in junior high school about quadratic equation of one variable
The speed limit of a 400km expressway is 110km / h
Zhang: your speed is too fast. On average, you run 10km more per hour than me. You can finish the whole race in one hour less
Li: Although my speed is fast, the maximum speed is no more than 110% of my average speed
Please judge whether Master Li is speeding or not?

Suppose Master Zhang's average speed is x km / h and master Li's average speed is (x + 10) km / h
400/X=400/(X+10)+1
The solution is x ≈ 58 (negative value rounding off)
Master Li's average speed is 58 + 10 = 68
Master Li's maximum speed is 68 × 110% = 75 < 110%
Therefore, Master Li did not violate the law of speeding

If x ^ 2-2 (M + 1) x + m ^ 2 + 5 is a complete bisection, find the value of M

x^2-2(m+1)x+m^2+5=0
4(m+1)^2-4m^2-20=0
8m-16=0
m=2