IF `b^3+a^2c+ac^2=3abc`,find the relation between the roots of the equation `ax^2+bx+c=0`.

If a, b, c are in HP, find the relation between the roots of ax^2+bx+c=0 .

IF the equation 4x^2+2bx+c=0,b=0 , find the relation between the roots of the equation.

Let a,b,c be real numbers with ane0 and let alpha,beta be the roots of the equation ax^2+bx+c=0 . Express the roots of a^2cx^2+(b^3-3abc)x+ac^2=0 in terms of alpha,beta .

If b^2ge4ac for the equations ax^4+bx^2+c=0 then all the roots of the equation will be real if

If a,b,c are rational,if b^(2)-4ac=0 then nature of the roots of the equation ax^(2)+bx+c=0(a!=0) are

If b^(2) - 4ac gt 0, then find the nature of roots of quadratic equations ax^(2) + bx+ c =0

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for