The locus of the point P =(a,b) where a , b are real numbers such that the root of `x^3+ax^2+bx+a=0` are in arithmetic progression is

The locus of the point P = (a, b) where a, b are real numbers such that the roots of x^(3)+ax^(2)+bx+a =0 are in arithmetic progression is -

If a,b,c are real numbers and Delta >0 then the roots of ax^(2)+bx+c=0 are

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

If a,b,c are positive real numbers, then the roots of the equation ax^(2) + bx + c =0

a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=0 and dx ^(2) + 2 ex + f =0 have a common root, pairs (a,b) of real numbers such that d/a,e/b,f/c are in arithmetic progression.

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then