If the zeroes of the polynomial 3×2 –11x+k are reciprocal to each other, then the value of k is [ ]​

Question

If the zeroes of the polynomial 3×2 –11x+k are reciprocal to each
other, then the value of k is
[ ]​

in progress 0
Eliza 1 month 2021-09-14T23:10:23+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-14T23:11:34+00:00

    EXPLANATION.

    • GIVEN

    zeroes of the polynomial = 3x² – 11x + k

    are reciprocal to each other.

    Find value of k is.

    according to the question,

    products of zeroes of quadratic polynomial

    => ab = c/a

    quadratic polynomial are reciprocal to each

    other => a X 1/a = 1

    => 1 = c/a

    => 1 = k/3

    => k = 3

    Therefore,

    Value of k = 3

    Formula of quadratic polynomial.

    => sum of zeroes of quadratic polynomial.

    => a + b = -b/a

    => products of zeroes of quadratic polynomial.

    => ab = c/a

    Equation of quadratic polynomial.

    => x² – ( a + b )x + ab

    0
    2021-09-14T23:11:59+00:00

    Answer:

    Let one root of the given that other zero is Reciprocal the one zero.

    So,

    Other zero=1/Alpa.

    Given polynomial is 5x

    2

    +13x+k=0.

    Here,

    A=coefficient of x

    2

    B=coefficient of x

    And,C=constant term.

    Product of zeroes =C/A

    Alpha ×1/Alpha =K/5

    1=K/5

    K=5

    Then,

    We get k=5.

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