Ifa,ß are the zeros of the polynomial 3×2 + 5x + k such that a² + B2 +  \alpha \beta =19/9 then find the v

Question

Ifa,ß are the zeros of the polynomial 3×2
+ 5x + k such that a² + B2 +
 \alpha  \beta
=19/9
then find the value of k.​

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Savannah 2 weeks 2021-09-09T15:21:45+00:00 1 Answer 0 views 0

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    2021-09-09T15:23:22+00:00

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    amishagour

    28.06.2018

    Math

    Secondary School

    +5 pts

    Answered

    if alpha and beta are the zeroes of the polynomial x2-5x+k, such that alpha-beta=1, find the value of k

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    Aurora34 Genius

    We know that,

    sum of zeroes= -b/a

    \alpha + \beta = 5

    ________________________(1)

    also,

    product of zeroes= c/a

    \alpha \beta = k

    _______________________(2)

    Given:

    \alpha – \beta = 1

    ______________________(3)

    from (1) and (3)

    \alpha + \beta = 5 \\ \alpha – \beta = 1 \ \: \: \: \: (on \: \: adding) \\ …………….. \\ 2 \alpha = 6 \\ \\ \alpha = 3 \\ \\ put \: \: this \: \: in \: \: (3) \\ \\ 3 – \beta = 1 \\ \\ – \beta = – 2 \\ \\ \beta = 2

    now put this value in (3)

    \alpha \beta = k \\ \\ 2 \times 3 = k \\ \\ 6 = k

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