Q1
The zero of the polynomial x-5 is:
A5
B-5
C0
D1
CBSEClass 9 (CBSE)MathematicsCh 2 · Topic 2
Zeroes of a Polynomial and Factorisation
Learning to find the zeroes of a polynomial and factorise it.
Core concept
This relationship, known as the Factor Theorem, allows polynomials to be factorised systematically: if we can find a zero of a polynomial, we automatically know one of its factors, and can use polynomial division to find the remaining factor(s). For a quadratic polynomial, there can be up to two zeroes (or none among real numbers, in some cases), corresponding to the points where its graph, a parabola, crosses the x-axis.
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CBSE class 9 zeroes of a polynomial and factorisation
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• A zero of a polynomial is a value making the polynomial equal to zero.
• For p(x)=x-2, the zero is x=2, since p(2)=0.
• Factor Theorem: if 'a' is a zero of p(x), then (x-a) is a factor of p(x).
• A quadratic polynomial can have up to two zeroes, corresponding to x-axis crossings on its graph.