Find the condition in order that the equation `ax^4+4bx^3+6cx^2+4dx+e=0`
may have a pair of equal roots .

Find the condition that the equation x^3 + bx^2 + cx +d =0 may have two roots equal but of opposite sign.

Find the condition that the roots of the equation ax^3+bx^2+cx+d=0 are in A.P.

FIND that condition that the roots of equation ax^3+3bx^2+3cx+d=0 may be in G.P.

FIND that condition that the roots of equation ax^3+3bx^2+3cx+d=0 may be in G.P.

Find the condition that the roots of ax^3+bx^2+cx+d=0 are in H.P.

Find the condition that quadratic equations x^(2)+ax+b=0 and x^(2)+bx+a=0 may have a common root.

The condition that the equation ax^(2)+bx+c=0 may have one root is the double the other is

Find the condition that the ratio between the roots of the equation ax^(2)+bx+c=0 may be m:n.

Find the condition on a,b,c,d such that equations 2ax^(3)+bx^(2)+cx+d=0and2ax^(2)+3bx+4c=0 have a common root.