If a,  b, c∈R and 1 is a root of the equation ax2+bx+c=0  then the equation 4ax2+3bx+2c=0,  c≠0  has roots which are:

1 is a root of ax2+bx+c=0 ⇒a+b+c=0 D of 4ax2+3bx+2c=0  is     b2-4ac    =9b2−32ac=9(a+c)2−32ac        =c2{9(a/c)2−14(a/c)+9}       =c2{(3(a/c)−7/3)2+9−49/9}>0⇒  roots are real and distinct