Multiple choice

How many real roots does the equation a3 + 5a + 1 = 0 have?

  1. 3

  2. 2

  3. 1

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let f(a) = a^3 + 5a + 1. The derivative f'(a) = 3a^2 + 5, which is always positive. Thus, the function is strictly increasing and crosses the x-axis exactly once.

AI explanation

For the cubic equation a^3 + 5a + 1 = 0, we analyze the function f(a) = a^3 + 5a + 1. The derivative of this function is f'(a) = 3a^2 + 5, which is always positive for all real numbers. Because the function is strictly increasing, it can cross the x-axis exactly one time. Therefore, the equation has exactly 1 real root.

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