方法多:1)可这样做,据条件,a,2a为其根代入18*a^3+9*a^2-74*a+40 = 0,144*a^3+36*a^2-148*a+40 = 0,消去3,2次项即得;{x1=a = 2/3},{x2=2a= 4/3},{x3 = -5/2};
2)4个根有2个重根a,2个重根b,说明:原方程是一个平方式;可设为(x^2+p*x+q)^2=x^4+4x^3+10x^2+12x+9,则有2p=4;q^2=9;2pq=12,所以p=2,q=3;所以有:
x^2+2*x+3=0,所以a=-1+sqrt(2)*I,b=-1-sqrt(2)*I;或者a=-1-sqrt(2)*I,b=-1+sqrt(2)*I.