Polynomials

Topics in this chapter

• Polynomial Basics and Degree
• Geometrical Meaning of Zeroes
• Finding Zeroes and Factorisation
• Polynomial Division and Remainders
• Zeroes and Coefficients
• Forming Polynomials from Zeroes
• Quadratic Polynomial Applications

Cheat sheet

Practice questions

1. Question 1Q-0EC414

   If one zero of the quadratic polynomial $p(x) = 4x^2 - 8kx - 9$ is negative of the other, then the value of $k$ is:

   1. A.0
   2. B.-1
   3. C.1
   4. D.2
   See the answer and solution
2. Question 2Q-717D51

   The graph of $y = p(x)$ is given, where $p(x)$ is a polynomial. If the graph intersects the x-axis at exactly 3 distinct points, then the degree of $p(x)$ is at least:

   1. A.1
   2. B.2
   3. C.3
   4. D.4
   See the answer and solution
3. Question 3Q-7D4C60

   If $\alpha$ and eta are the zeroes of the polynomial $f(x) = x^2 - 5x + k$ such that \alpha - eta = 1, find the value of $k$.

   1. A.4
   2. B.5
   3. C.6
   4. D.7
   See the answer and solution
4. Question 4Q-DF85C4

   If the squared difference of the zeroes of the quadratic polynomial $f(x) = x^2 + px + 45$ is equal to 144, find the value of $p$.

   1. A.±12
   2. B.±18
   3. C.±6
   4. D.±9
   See the answer and solution
5. Question 5Q-174CE2

   If the sum of the zeroes of the quadratic polynomial $p(x) = kx^2 - 3x + 5$ is equal to twice their product, then the value of $k$ is:

   1. A.-3/10
   2. B.3/10
   3. C.-10/3
   4. D.10/3
   See the answer and solution