If α and β are the zeros of the quadratic polynomial , find a quadratic polynomial whose zeros are .
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 = = = [Using (a + b)2 = a2 + b2 + 2ab]
⇒ = = = -4
Product of the zeros of new eqn = = 4