How many real roots does the equation have?

Answer and explanation

Correct answer: D.

  1. Step 1: Let . Then , , , .
  2. Step 2: The sign changes between and , between and , and between and , so there are three roots.
  3. Step 3: A cubic has at most three roots, so exactly .
Answer
.
Why not the others: The three sign changes give a root in each interval, so and are too few. A cubic always has at least one real root, so is impossible, and it cannot have more than three, so is impossible.

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