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 ( x+ 5) and ( x - 3) are the factors of ax^(2) + bx + c , then values of a,b and c are

Let |(x,2,x),(x^(2),x,6),(x,x,6)| = ax^(4) + bx^(3) + cx^(2) + dx + e Then, the value of 5a + 4b + 3c + 2d + e is equal to

If ax^(2)+ bx +c and bx ^(2) + ax + c have a common factor x +1 then show that c=0 and a =b.

If x^2+ax+1=0 is a factor of ax^3+ bx + c , then which of the following conditions are not valid

The integrating factor of (dy)/(dx) +2 y/x = e^(4x) is :

If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that a, b, c and d are in G.P.

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

Let three quadratic equations ax^(2) - 2bx + c = 0, bx^(2) - 2 cx + a = 0 and cx^(2) - ax + b = 0 , all have only positive roots. Then ltbr. Which of these are always ture?