Question

一个初中方程题

设方程3x²-5x+a=0的两根为X1和X2，且6X1+X2=0求a的值

用韦达定理做

Answer 1

根据韦达定理
x1+x2=5/3
6x1+x2=0
5x1+x1+x2=0
5x1+5/3=0
x1=-1/3

x2=5/3-(1/3)=5/3+1/3=2

x1x2=a/3
-1/3*2=a/3
a=-2

Answer 2

X1+X2=5/3
6X1+X2=0
X1=-1/3;X2=2
a=X1X2=-2/3

Answer 3

因为根据韦达定理有 x1 + x2= -(-5)/3 , x1 * x2 = a/3

又因为 6x1 + x2 = 0

所以 x1 = -1/3 x2 = 2 a = -2