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} = a^{2} + b^{2} + 2ab]

⇒ = =

Product of the zeros of new eqn = =

⇒ = = =

⇒ = =

)

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