The condition that the roots of the equation `ax^3+bx^2+cx+d=0` may be in `A.P.`, if (i) `2b^3+27a^2d=9abc` (ii) `2b^3+27a^2d=-9abc` (iii) `2b^3-27a^2d=9abc` (iv) `2b^3-27a^2d=-9abc`

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

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

If 1,2,3 and 4 are the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0, then a+2b+c=

If the zeros of the polynomial f(x)=ax^(3)+3bx^(2)+3cx+d are in A.P. prove that 2b^(3)-3abc+a^(2)d=0

If the zeros of the polynomial f(x)=ax^(3)+3bx^(2)+3cx+d are in A.P.then show that 2b^(3)-3abc+a^(2)d=0

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.

27a^3b^3-45a^4b^2

If one root of the equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0, (a, b, c in R) is common, then the value of ((a^(3)+b^(3)+c^(3))/(abc))^(3) is

If 27a+9b+3c+d=0 then the equation 4ax^(3)+3bx^(2)+2cx+d has at leat one real root lying between

If the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ca)x+(c^(2)-ab)=0 are equal then the condition is (i)a+b+c=0(ii)a^(3)+b^(3)+c^(3)-3abc=0 (iii) a=0 or a^(3)+b^(3)+c^(3)-3abc=0 (iv) b=0 or a^(3)+b^(3)+c^(3)-3abc=0