If the roots of the equation `x^3+3ax^2+3bx+c=0` are in `H.P.`, then (i) `2b^2=c(3ab-c)` (ii) `2b^3=c(3ab-c)` (iii) `2b^3=c^(2)(3ab-c)` (iv) `2b^2=c^(2)(3ab-c)`

If the roots of the equation x^(3) + ax^(2) + bx + c = 0 are in A.P., 2a^(3) - 9ab =

If the roots of the equation x^(3)+3ax^(2)+3bx+c=0 are in H.P., then x^(3)+3ax^(2)+3bx+c=0 are in (3ab-c)( iii) 2b^(3)=c^(2)(3ab-c)( iv) 2b^(2)=c^(2)(3ab-c)

If a,b,c are the roots of the equation x^(3)-3x^(2)+3x+7=0, then the value of det[[2bc-a^(2),c^(2),b^(2)c^(2),2ac-b^(2),a^(2)b^(2),a^(2),2ab-c^(2)]] is

Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 are equal if either b=0 or , a^3+b^3+c^3-3abc=0

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

If the roots of the equation (c^(2)-ab)x^(3)-2(a^(2)-bc)x+b^(2)-ac=0 are real and equal prove that either a=0 (or) a^(3)+b^(3)+c^(3)=3"abc" .

If the roots of the equation (c^(2)-ab)x^(2)-2(a^(2)-bc)x+b^(2)-ac=0 are equal,prove that either a=0 or a^(3)+b^(3)+c^(3)=3abc

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0