If a, b, c R and 1 is a root of equation a x^2+b x+c=0 , then the curve y=4 a x^2+3 b x+2 c, a 0 intersect x -axis at

Step-by-step solution

Given a x^2+b x+c=0 aligned & a x^2=-b x-c & Now, consider & y=4 a x^2+3 b x+2 c & =4[-b x-c]+3 b x+2 c & =-4 b x-4 c+3 b x+2 c & =-b x-2 c aligned Since, this curve intersects x -axis put y=0 , we get aligned & -b x-2 c=0 -b x=2 c & x= -2 c b aligned Thus, given curve intersects x -axis at exactly one point.