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Math Help - show equation has exactly one real root

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    show equation has exactly one real root

    show that the equation 3x +2cosx + 5 = 0 has exactly one real root? incorporate the intermediate value theorem and rolles theorem.
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    Quote Originally Posted by element View Post
    show that the equation 3x +2cosx + 5 = 0 has exactly one real root? incorporate the intermediate value theorem and rolles theorem.
    Let f(x) = 3x + 2 cos x + 5.

    Use IVT to show there's at least one root.

    Now assume two roots x = a and x = b, that is f(a) = f(b) = 0. Apply Rolles Theorem over the interval [a, b] and show that you get a false conclusion for real numbers.
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