1) Find quad. polynomial whose zeros are (2+√3) and (2-√2)​

Question

1) Find quad. polynomial whose zeros are
(2+√3) and (2-√2)​

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Aubrey 3 weeks 2021-08-20T04:46:00+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-20T04:47:30+00:00

    \huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}

    Given that,

    Find quadratic polynomial whose zeroes are

    (2 + √3) and (2 – √2).

    Let,

    • α = (2 + √3)
    • ß = (2 – √2)

    ☯ α + ß = (2 + √3) + (2 – √3) = 2 + √3 + 2 – √3 = 4

    ☯ αß = (2 + √3)(2 – √3) = (2)² – (√3)² = 4 – 3 = 1

    General form of quadratic polynomial is

    ↪ x² – (α + ß)x + αß = 0

    Substitute the zeroes…

    ➡ x² – (4)x + (1) = 0

    ➡ x² – 4x + 1 = 0

    \underline{\boxed{\bf{\purple{∴ The\;Quadratic\;polynomial\;is\;`` \:  x² - 4x + 1 = 0 \:  "}}}}

    Step-by-step explanation:

    <marquee behaviour-move><font color="green pink"><h1># PLEASE MARK ME AS BRAINLIEST✌✌✌</ ht></marquee>

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