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Worksheet: Using Descartes's Rule of Signs

Q1:

Using Descartesโ€™s rule of signs, find which of the following describes the possible real zeros of ๐‘“ ( ๐‘ฅ ) = โˆ’ 6 ๐‘ฅ + 3 ๐‘ฅ + 7 ๐‘ฅ โˆ’ 1 3 2 .

  • A ๐‘“ ( ๐‘ฅ ) has 0 positive zeros and either 3 or 1 negative zeros.
  • B ๐‘“ ( ๐‘ฅ ) has 1 positive zero and 0 negative zeros.
  • C ๐‘” ( ๐‘ฅ ) has 1 positive zero and either 2 or 0 negative zeros.
  • D ๐‘“ ( ๐‘ฅ ) has either 2 or 0 positive zeros and one negative zero.
  • E ๐‘“ ( ๐‘ฅ ) has either 3 or 1 positive zeros and 0 negative zeros.

Q2:

Using Descartesโ€™s rule of signs, find which of the following describes the possible real zeros of ๐‘” ( ๐‘ฅ ) = โˆ’ ๐‘ฅ โˆ’ 3 ๐‘ฅ + 4 ๐‘ฅ + 9 ๐‘ฅ โˆ’ 4 4 3 2 .

  • A ๐‘” ( ๐‘ฅ ) has 0 positive zeros and either 2 or 0 negative zeros.
  • B ๐‘” ( ๐‘ฅ ) has either 2 or 0 positive zeros and 0 negative zeros.
  • C ๐‘” ( ๐‘ฅ ) has either 3 or 1 positive zeros and 1 negative zero.
  • D ๐‘” ( ๐‘ฅ ) has either 2 or 0 positive zeros and either 2 or 0 negative zeros.
  • E ๐‘” ( ๐‘ฅ ) has 1 positive zero and either 3 or 1 negative zeros.

Q3:

Using Descartesโ€™s rule of signs, find which of the following describes the possible real zeros of โ„Ž ( ๐‘ฅ ) = 3 ๐‘ฅ + 2 ๐‘ฅ โˆ’ 3 ๐‘ฅ + ๐‘ฅ + 6 ๐‘ฅ + 2 5 4 3 2 .

  • A โ„Ž ( ๐‘ฅ ) has either 2 or 0 positive zeros and 1 negative zero.
  • B โ„Ž ( ๐‘ฅ ) has 0 positive zeros and either 3 or 1 negative zeros.
  • C โ„Ž ( ๐‘ฅ ) has either 3 or 1 positive zeros and 0 negative zeros.
  • D โ„Ž ( ๐‘ฅ ) has either 2 or 0 positive zeros and either 3 or 1 negative zeros.
  • E โ„Ž ( ๐‘ฅ ) has either 3 or 1 positive zeros and either 2 or 0 negative zeros.