SPS SPS SM Statistics 2022 February — Question 1

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2022
SessionFebruary
TopicFactor & Remainder Theorem
TypeProve root count with given polynomial

1. Answer all the questions. $$f ( x ) = 3 x ^ { 3 } - 7 x ^ { 2 } + 7 x - 10$$
  1. Use the factor theorem to show that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\)
  2. Find the values of the constants \(a , b\) and \(c\) such that $$\mathrm { f } ( x ) \equiv ( x - 2 ) \left( a x ^ { 2 } + b x + c \right)$$
  3. Using your answer to part (b) show that the equation \(\mathrm { f } ( x ) = 0\) has only one real root.
    [0pt] [BLANK PAGE]