Page 1 - Lesson Notes-Relationhip between Zeroes and coefficients Ch-2 (Polynomals)

SAI International School

Class-X

Mathematics
Chapter-2: Polynomials
Lesson Notes

Sub topics: Relationship between Zeroes and Co-efficients of a
polynomial

Zeroes of a Polynomial:
The value of the variable for which a polynomial becomes zero is called
as a zero of that polynomial.
OR A real number k is said to be zero of a polynomial p(x), if p(k)=0

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Q. What is the value of p(x) = x –3x – 4 at x = –1?
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We have : p(–1) = (–1) –{3 × (–1)} – 4 = 0
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Also, p(4) = 4 – (3x4) – 4 = 0.

As p(–1) = 0 and p(4) = 0, So, –1 and 4 are called the zeroes of the quadratic
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polynomial x – 3x – 4.

Relationship between Zeroes and Co-efficients of a Linear
polynomial

Standard form a Linear Polynomial in one variable is : ax + b, where a ≠ 0 , a and b
are real numbers.

Here, a is the coefficient of x and b is the constant term.

To find the zero of a polynomial, take the polynomial = 0.

Let ax + b = 0

 ax = – b
− b
 x = .
a

− b
Therefore, the zero of the linear polynomial ax + b is .
a

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