Question

已知方程x2+mx+n=0的两根之比为1：2,根的判别式值是1,求做以m,n为两根的方程.

Answer 1

x^2+mx+n=0

x1+2x1=-m,x1*2x1=n

x1=-m/3,(x1)^2=n/2

(m/3)^2=n/2

m^2=9n/2

△=m^2-4n=1

m^2=4n+1

9n/2=4n+1

n=2

m=3或m=-3

n=2,m=3

所求方程为x^2-5x+6=0

n=2,m=-3

所求方程为x^2+x-6=0