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Home >> Polynomials >> Find Zero of Polynomial >>

Find Zero of Polynomial

Algebraic Expression Algebraic Equation Ordering of Polynomials Types of Polynomials Addition of Polynomials
Subtraction of Polynomials Multiplication of Polynomials Division of Polynomials Types of Degree / Powers in Polynomials Difference between Polynomials of Integers & Rationals
Find Value of Polynomial Find Zero of Polynomial Remainder Theorem in Polynomial Linear Equations Quadratic Equation
Factoring of Quadratic Polynomials



Before you understand how to find zero of polynomial, you are advised to read:

What is Value of Polynomial ?

What is Zero of Polynomial ?
When with the value of a variable we get value of the polynomial equals to 0 (zero), then said value of variable is known as Zero of Polynomial .

Or we can say that:
Zero of a polynomial p(x) is a number 'c' such that p(c) = 0

Or this can also be written as:
If p(c) = 0, then 'c' is referred to as Zero of Polynomial p(x)

Lets study the following examples to understand how to find the zero of polynomial.

Example 1: Check whether x = 2 or x = 3, is the Zero of Polynomial x3 + x - 10
Solution: Given polynomial is:
p(x) = x3 + x - 10

If x = 2, find the value of p(x) and we get:
p(2) = (2)3 + 2 - 10
= 8 + 2 - 10
= 10 - 10
= 0

If x = 3, find the value of p(x) and we get:
p(3) = (3)3 + 3 - 10
= 27 + 3 - 10
= 30 - 10
= 20

No, you can observe that when x = 2, we get p(x) = 0.
Hence, 2 is referred to as Zero of Polynomial x3 + x - 10



Example 2: Check whether t = 3 or t = (-3), is the Zero of Polynomial t2 - t - 12
Solution: Given polynomial is:
p(t) = t2 - t - 12

If t = 3, find the value of p(t) and we get:
p(3) = (3)2 - 3 - 12
= 9 - 3 - 12
= 9 - 15
= (-6)

If t = (-3), find the value of p(t) and we get:
p(-3) = (-3)2 - (-3) - 12
= 9 + 3 - 12
= 12 - 12
= 0

No, you can observe that when t = (-3), we get p(t) = 0.
Hence, (-3) is referred to as Zero of Polynomial t2 - t - 12





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