Worksheet: Polynomial Equations and the Rational Zeros Theorem

In this worksheet, we will practice solving real-world problems involving polynomial equations.


The cross-section of a skate banister, shown in the diagram, can be modeled with the polynomial function ( 𝑑 ) = 𝑑 + 5 2 𝑑 7 4 𝑑 + 7 8 , where is the height above the ground and 𝑑 is the horizontal distance from point 𝐴 .

Using the rational zeros theorem or otherwise, determine the horizontal distance between point 𝐴 and point 𝐵 given that point 𝐵 is 1 2 m above the ground.

  • A 1 8 m
  • B 1 4 m
  • C 1 m
  • D 1 2 m
  • E 3 m


The value of an investment 𝐼 in a given start-up business is predicted to be given over time by the function 𝐼 = 𝐼 𝑥 + 0 . 3 𝑥 1 0 . 1 𝑥 + 1 2 . 5 𝑥 2 . 1 𝑥 + 1 , where 𝑥 is the number of decades after the investment.

The graph shows that the investment is predicted to first lose value. Given that it is predicted that the gain will be positive after less than a decade, determine how many years it will take for the investment to first return to the value of 𝐼 .

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