Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots V5 and 2?

Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots
V5 and 2?

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Hưng Khoa 5 years 2021-07-18T22:06:14+00:00 1 Answers 68 views 0

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  1. phucdien
    0
    2021-07-18T22:07:27+00:00
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    Answer:

    f(x) = 3x^{3} - 6x^{2} - 15x + 30

    Step-by-step explanation:

    If  \sqrt{5}  is a root, then so is –\sqrt{5}

    f(x) = 3(x + \sqrt{5})(x – \sqrt{5})(x – 2)

         = 3(x^{2} - 5)(x - 2)

         = 3(x^{3} - 2x^{2} - 5x + 10)

         = 3x^{3} - 6x^{2} - 15x + 30

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )