If `(x ^(2) -1)` is a factor of `ax ^(4) + bx ^(3) + cx ^(2) + dx +e,` then show that `a + c +e =b +d=0`

If 3/4, -5/2, 1/2 , -3 are the roots of ax^(4) + bx^(3) + cx^(2) + dx + e = 0 then the roots of ex^(4) + dx^(3) + cx^(2) + bx + d = 0 are

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

If -2, 5, 7, - 11 are the roots of ax^(4) + bx^(3) +cx^(2) + dx + e = 0 then the roots of ax^(4) - bx^(3) + cx^(2) - dx + e = 0 are

The degree of the polynomial ax^(4) + bx^(3) + cx^(2) + dx + e is ………..

If 2,5,7,-4 are the roots of ax^4 + bx^3 + cx^2 + dx +e=0 then the roots of ax^4 - bx^3 + cx^2 -dx +e=0 are

IF (x-2) is a common factor of the expression x^2 + ax + b and x ^2 + cx + d then (b-d) /( c-a ) =

If sin^(2) A = x and prod_(r = 1)^(4) sin (rA) = ax^(2) + bx^(3) + cx^(4) + dx^(5) then the value of a + b + c + d must be

If alpha, beta, gamma, delta are roots of ax^(4) + 4bx^(3) + 6cx^(2) + 4dx + e = 0, then sum alpha^(2) beta =

If int x^(3) e^(-x) " dx = " - e^(-x) [ ax^(3) + bx^(2) + cx + d] K then (a, b,c,d) =