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If α and β are the zeros of the quadratic polynomial , find a polynomial whose roots are (i)
(ii)
.
(i)
A quadratic equation when sum and product of its zeros is given by:
, where k is a constant
Sum of the roots = =
=
=
Product of the roots = =
=
Sum of the zeros of new eqn = =
Product of the zeros of new eqn = =
(ii) A quadratic equation when sum and product of its zeros is given by:
, where k is a constant
Sum of the roots = =
=
=
Product of the roots = =
=
Sum of the zeros of new eqn = =
=
=
=
Product of the zeros of new eqn = =
=
=
=
Therefore eqn is:
=
=
=
= 0