Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Number and Type of Roots of a Polynomial

Q1:

Find, by factoring, the zeros of the function 𝑓 ( π‘₯ ) = 1 2 π‘₯ βˆ’ 1 4 π‘₯ βˆ’ 6 2 .

  • A 1 3 , βˆ’ 3 2
  • B βˆ’ 1 3 , βˆ’ 3 2
  • C 2 3 , 3 4
  • D βˆ’ 1 3 , 3 2
  • E βˆ’ 2 3 , 3 4

Q2:

How many roots does the polynomial 5 π‘₯ + 4 π‘₯ βˆ’ 1 3 have?

Q3:

Which of the following lists contain all the roots of 4 π‘₯ βˆ’ 1 0 π‘₯ βˆ’ 7 6 π‘₯ + 7 0 π‘₯ + 3 0 0 4 3 2 ?

  • A βˆ’ 3 , 2 , 5 , 5 2
  • B 3 , 2 , βˆ’ 5 , βˆ’ 5 2
  • C βˆ’ 3 , βˆ’ 2 , 5 , βˆ’ 5 2
  • D βˆ’ 3 , βˆ’ 2 , 5 , 5 2

Q4:

Is ( π‘₯ βˆ’ π‘Ž ) a factor of 𝑓 ( π‘₯ ) given that 𝑓 ( π‘Ž ) = 3 ?

  • Ano
  • Byes

Q5:

Find, by factoring, the zeros of the function 𝑓 ( π‘₯ ) = 6 π‘₯ + 3 3 π‘₯ βˆ’ 6 3 π‘₯ 4 3 2 .

  • A 7 , 0 , βˆ’ 3 2
  • B βˆ’ 7 , 0 , βˆ’ 3 2
  • C βˆ’ 3 , 0 , 7 2
  • D βˆ’ 7 , 0 , 3 2
  • E 3 , 0 , βˆ’ 7 2

Q6:

Which of the following are roots of 6 π‘₯ + 4 3 π‘₯ βˆ’ 1 6 9 π‘₯ βˆ’ 9 8 8 π‘₯ + 1 9 4 8 π‘₯ + 1 6 8 0 5 4 3 2 ?

  • A βˆ’ 7 , βˆ’ 5 2 and βˆ’ 2 3
  • B6, 5 2 and 2 3
  • C4, 2 5 and βˆ’ 2 3
  • D βˆ’ 6 , 5 2 and βˆ’ 2 3
  • E4, βˆ’ 6 and 7

Q7:

Is ( π‘₯ βˆ’ π‘Ž ) a factor of 𝑓 ( π‘₯ ) given that 𝑓 ( π‘Ž ) = 0 ?

  • Ayes
  • Bno