Question

If x^2-1 is a factor of ax^3+bx^2+cx+d then show that a+c=0

Answer 1

if
$x^2 - 1 \: is \: a \: factor \: of \: the \: given \: polynomial. \\ then(x - 1)(x +1) \: is \: aso \: factor \: of \: the \: polynomial. \\ then \: two \: of \: its \: zeroes \: are \: - 1 \: and \: + 1 \: putting \: these \: values \: of \: x \: in \: t he \: given \: polynomia \: we \: get \: \\ (1) \: - a + b - c + d = 0 \\ (2) \: a + b + c + d = 0 \\ subtracting \: (2) \: from \: (1) \: we \: get \: \\ a + c = 0 \\ hence \: verified$