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

If x-1 is a factor of 2x^(3)+ax^(2)+2bx+1 and 2a-b=4 . Find the values of a and b.

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

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c , then a, b, c, d are in

if x^2+x+1 is a factor of ax^3+bx^2+cx+d then the real root of ax^3+bx^2+cx+d=0 is : (a) -d/a (B) d/a (C) a/b (D)none of these

If |ax^2 + bx+c|<=1 for all x is [0, 1] ,then

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.

Differentiate sin^(n) (a x^(2) + bx + c)

f(x)= bx^(2) + cx and d and f(x+ 1) - f(x)= 8x + 3 then…….