Mathematics

Question

The degree of the polynomial function f(x) is 4.

The roots of the equation f(x)=0 are −2, −1, 1 and 3.

Which graph could be the graph of f(x)?
The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −2, −1, 1 and 3. Which graph could be the graph of f(x)?

1 Answer

  • Answer:

    Option A

    Step-by-step explanation:

    Degree of the polynomial function = 4

    That means highest degree term of the given polynomial has power = 4

    If the roots of a quadratic polynomial are a, b, c, d then the polynomial function will be,

    f(x) = (x - a)(x - b)(x - c)(x - d)

    It's given in the question that roots are x = -2, -1, 1 and 3

    Therefore, polynomial function will be,

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

    From the given options, graph A shows that the graph intersects the x-axis at x = -2, -1, 1 and 3

    Therefore, Option A will be the answer.

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