If a & ß are the zeros of f(x) = x² + px +q, then a polynomial having 1/a & 1/ß as its zeros is​

Question

If a & ß are the zeros of f(x) = x² + px +q, then a
polynomial having 1/a & 1/ß as its zeros is​

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Peyton 1 month 2021-08-23T05:16:20+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-23T05:17:42+00:00

    Answer:

    If the polynomial f(x)=x

    2

    −px+q has the roots as α and β.

    Then the equation having the roots as

    α

    1

    and

    β

    1

    is f(

    x

    1

    ).

    ⇒ f(

    x

    1

    )=(

    x

    2

    1

    )−p(

    x

    1

    )+q

    ⇒ f(

    x

    1

    )=qx

    2

    −px+1.

    Therefore the equation having

    α

    1

    and

    β

    1

    as roots is qx

    2

    −px+1.

    Step-by-step explanation:

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