If a, ß are zeroes of P(x) = x² – 6x + k, such that a² + ² = 20 then find the value of k.​

Question

If a, ß are zeroes of P(x) = x² – 6x + k, such that a² + ² = 20 then find the value of k.​

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Liliana 2 months 2021-07-27T14:31:38+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-27T14:33:30+00:00

    \sf{\huge{\underline{\green{Given :-}}}}

    • a, ß are zeroes of P(x) = x² – 6x + k, such that α² + β² = 20 .

    \sf{\huge{\underline{\green{To\:Find :-}}}}

    • The value of k.

    \sf{\huge{\underline{\green{Answer :-}}}}

    We have,

    f(x) = x2 – 6x + k

    α² + β² = 20

    ➝ ( α + β )² – 2αβ = 20 ——(1)

    α + β = -b/a

    ➝ -(-6)/1

    6

    αβ = c/a

    ➝ k/1

    k

    Putting Value in (1),

    ( α + β )² – 2αβ = 20

    ➝ ( 6 )² – 2k = 20

    ➝ 36 – 2k = 20

    ➝ – 2k = 20 – 36

    ➝ – 2k = -16

    ➝ k = -16/-2

    k = 8

    The value of k is 8.

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