Multiple choice

Let $x_1, x_2, ....., x_6$ be the roots of the polynomial equation $x^6+2x^5+4x^4+8x^3+16x^2+32x+64=0$. Then.

  1. $|x_i|=2$ for exactly one value of $i$
  2. $|x_i|=2$ for exactly two values of $i$
  3. $|x_i|=2$ for all values of $i$
  4. $|x_i|=2$ for no value of $i$
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C Correct answer
AI explanation

Rewrite the given polynomial as a geometric progression to find x^6 equals negative 64, which means the magnitude of x is the sixth root of 64. Since the absolute value of negative 64 is 64, the sixth root yields an absolute value of 2. Therefore, the magnitude of every root x_i is 2.

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