Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

find a polynomial of degree 3 that's zeros 1,2 and -3 and in which the coefficient of x is -2?

could you please help me with this; I don't really understand this question. First correct answer gets best answer award

thank you !! 

3 Answers

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    f(x) = -2 * (x - 1) * (x - 2) * (x - (-3))

    f(x) = -2 * (x - 1) * (x - 2) * (x + 3)

    f(x) = -2 * (x^2 - 3x + 2) * (x + 3)

    f(x) = -2 * (x^3 + 3x^2 - 3x^2 - 9x + 2x + 6)

    f(x) = -2 * (x^3 - 7x + 6)

    f(x) = -2x^3 + 14x - 12

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  • 2 months ago

    If 1 is a root, it means that you can factorize: (x - 1)

    If 2 is a root, it means that you can factorize: (x - 2)

    If - 3 is a root, it means that you can factorize: (x + 3)

    It gives us:

    = (x - 1).(x - 2).(x + 3)

    = (x² - 2x - x + 2).(x + 3)

    = (x² - 3x + 2).(x + 3)

    = x³ + 3x² - 3x² - 9x + 2x + 6

    = x³ - 7x + 6 → given that the coefficient of x is - 2 ? Perhaps the coefficient of x³ ?

    = - 2.(x³ - 7x + 6)

    = - 2x³ + 14x - 12

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  • 2 months ago

    f(x) = a(x - 1)(x - 2)(x + 3) 

    f(x) = a( x³ - 7x + 6 )

    f(x) = ax³ - 7ax + 6a

    -7a = -2

    ∴ a = 2/7

    f(x) = 2/7( x³ - 7x + 6 )

    f(x) = 2/7x³ - 2x + 12/7

    • JOHN
      Lv 7
      2 months agoReport

      This is a good answer with a good method. I would have given you the BA.

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