Multiple Choice Question (MCQ)

Let f (x) = ax^2 and g(x) = bx^4 for any value of x. If a and b are positive constants, for how many values of x is f (x) = g(x) ?

  1. ×

    None

  2. ×

    One

  3. ×

    Two

  4. Three

  5. ×

    Four

Collected in the board: Quartic Equations

Steven Zheng posted 6 hours ago

Answer

  1. For a quartic equation, it normally has four roots. But there're exceptions when it has duplicated root. In this case,

    f (x) = g(x) \implies ax^2 = bx^4

    Then

    ax^2 - bx^4 = 0

    x^2(a-bx^2) = 0

    Then

    x = 0, which represents two duplicate roots

    or

    x =\pm\sqrt{\dfrac{a}{b} }

    There for there are three roots for the equation.

    D is correct

Steven Zheng posted 6 hours ago

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