Multiple choice

The equation $x^7 + 3x^2 + 4x - 9 = 0$ has

  1. No real root

  2. All its roots real

  3. A unique root

  4. A unique irrational root
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Let f(x) = x^7 + 3x^2 + 4x - 9, and note that its derivative, f'(x) = 7x^6 + 6x + 4, is always strictly positive because an even power of x is non-negative and the linear term 6x has a minimum value. Because f'(x) > 0 for all real numbers, the function is strictly increasing and can cross the x-axis exactly once.

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