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15 November, 18:13

Which of the following is a polynomial with rootsnegative square root of 5, square root of 5, and 3

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  1. 15 November, 18:36
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    P (x) = x³ - 3x² - 5x + 15

    Step-by-step explanation:

    ∵ The roots of the polynomial are - √5, √5, 3

    ∴ The polynomial has 3 factors:

    (x - √5), (x + √5), (x - 3)

    ∴ P (x) = (x - √5) (x + √5) (x - 3)

    = (x² + √5x - √5x - 5) (x - 3)

    = (x² - 5) (x - 3) = x³ - 3x² - 5x + 15

    ∴ P (x) = x³ - 3x² - 5x + 15
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