1. What is the zero of the polynomial p(x) = x - 5?
- A5
- B-5
- C0
- D
Show answer
Answer: A) 5
Set p(x) = 0: x - 5 = 0, so x = 5.
Class 9 Zeroes of a Polynomial — practice questions with answers
Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Which value of x is NOT a zero of p(x) = (x - 2)(x + 3)?
- A3
- B2
- C-3
- DBoth 2 and -3 are zeroes
Show answer
Answer: A) 3
Zeroes occur when each factor is 0: x = 2 or x = -3. So x = 3 is not a zero.
3. Rohan sells x notebooks. His net profit (in Rupees) is modelled by p(x) = 15x - 600.
He breaks even (zero profit) when p(x) = 0.
How many notebooks must he sell to break even?
He breaks even (zero profit) when p(x) = 0.
How many notebooks must he sell to break even?
- A40
- B36
- C44
- D80
Show answer
Answer: A) 40
Set 15x - 600 = 0, so 15x = 600, giving x = 40 notebooks.
4. A polynomial p(x) = x² - 2x - 8 is plotted, and the curve cuts the x-axis at two points marked below.
Using the graph and a check, identify the two zeroes.
Using the graph and a check, identify the two zeroes.
- A-2 and 4
- B2 and 4
- C-4 and 2
- D-2 and -4
Show answer
Answer: A) -2 and 4
x² - 2x - 8 = (x - 4)(x + 2), zeroes 4 and -2. These match the x-axis crossings.
5. A polynomial p(x) = x³ - 6x² + 11x - 6 is known to have x = 1, x = 2 and x = 3 among its zeroes.
A student claims the SUM of all the zeroes equals the value you get by adding these three.
What is the sum of all the zeroes of p(x)?
A student claims the SUM of all the zeroes equals the value you get by adding these three.
What is the sum of all the zeroes of p(x)?
- A12
- B5
- C6
- D7
Show answer
Answer: C) 6
Check: p(x) = (x - 1)(x - 2)(x - 3), so the three zeroes are 1, 2, 3 and there are no others (degree 3). Their sum is 1 + 2 + 3 = 6.
Practise all 50 questions free →
10 free questions a day without an account — unlimited with a free account.