Question

初3的数学作业啊 帮帮忙啊

X^2+(K^2-25)X+K+2=0两根互为相反数,求K
6X^2+2X+A=0,一根比另一根大2,就A
方程X^2-(2M+1)X+M^2+3=0,两根平方和为25,求M

Answer 1

X^2+(K^2-25)X+K+2=0两根互为相反数,求K

x1+x2=-(k^2-25)=0

k^2=25,解得：k=±5

经检验，K=5不符题意，所以：K=-5

6X^2+2X+A=0,一根比另一根大2,就A

x1+x2=-2/6=-1/3
x1x2=A/6

设：x1-x2=2

所以：x1=(2-1/3)/2=5/6,x2=(-1/3-2)/2=-7/6

所以：A=6x1x2=6*5/6*[-7/6]=-35/6

方程X^2-(2M+1)X+M^2+3=0,两根平方和为25,求M

x1+x2=2m+1
x1x2=m^2+3

x1^2+x2^2=(x1+x2)^2-2x1x2=(2m+1)^2-2(m^2+3)=4m^2+4m+1-2m^2-6=2m^2+4m-5

所以：2m^2+4m-5=25

2m^2+4m-30=0

m^2+2m-15=0

(m+5)(m-3)=0

m1=-5

m2=3

经检验，m=-5不符题意，所以：m=3