Zero of a polynomial
- CBSE · NCERT Class 10, Ch 2 Polynomials
A zero of a polynomial p(x) is a value of x that makes p(x) equal to 0.
To test a number, put it in place of x and work out the value. If the answer is 0, that number is a zero. On a graph, the zeroes are where the curve y = p(x) meets the x-axis.
A polynomial of degree n has at most n zeroes. So a quadratic polynomial has at most 2, and a cubic has at most 3.
A small example
Take p(x) = x² - 5x + 6. Put x = 2: p(2) = 4 - 10 + 6 = 0. Put x = 3: p(3) = 9 - 15 + 6 = 0. So 2 and 3 are the zeroes. The graph of y = x² - 5x + 6 crosses the x-axis at (2, 0) and (3, 0).
Where marks go
Question 23 of CBSE's 2026-27 Maths Basic sample paper says 3 is a zero of 2x² - 3x + p. It asks for p and for the other zero, for 2 marks. The board's Maths Basic marking scheme for 2026-27 splits this into four half marks:
- Putting x = 3 and setting p(3) = 0.
- Finding p = -9.
- Writing the sum of the zeroes, 3 + β = 3/2.
- Finding the other zero, β = -3/2.
The first half mark is for the idea itself: a zero makes the polynomial equal to 0. Each later step then earns its own share under step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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