Find the condition that one root of `ax^2 + bx +c=0` shall be n times the other

The condition that one root of ax ^2+bx +c=0 may be n times the other root is

Find the condition that one root of ax^(2)+bx+c=0 may be four times the other.

The condition that one root of ax ^2 + bx +c=0 may be the double the other is

Find the condition that one root of ax^(2)+bx+c=0 may be (i) three tiems the other, (ii) n times the other, (iii) more than the other by h.

Prove that the condition that one root of ax^(2)+bx+c=0 may be the square of the other is b^(3)+a^(2)c+ac^(2)=3abc .

Find the condition that one of the roots of ax^(2) + bx+c may be Q (ii) thrice the other

Find the condition that one of the roots of ax^(2) + bx + c may be (i) negative of the other,

The condition that one root of ax^(3)+bx^(2)+cx+d=0 may be the sum of the other two is 4abc=

Find the condition that one of the roots of ax^(2) + bx + c may be (iii)reciprocal of the other.