HOW TO CHECK IF THE GIVEN VALUE IS THE ZERO OF THE POLYNOMIAL

About "How to Check if the Given Value is the Zero of the Polynomial"

How to Check if the Given Value is the Zero of the Polynomial :

Here we are going to see how to check if the given value is the zero of the polynomial.  

First, let us understand the meaning of the word zeroes. Zeroes means that is the only value which converts the polynomial as zero.

Alternative words for zeroes :

Roots, factors, solutions 

Let us look into some example problems based on the concept given above.

Example 1 :

Check whether 1/4 is a solution of the equation

3(x + 1) = 3(5 – x) – 2(5 + x)

Solution :

3(x + 1) = 3(5 – x) – 2(5 + x)

x = 1/4

3((1/4) + 1) = 3(5 – (1/4)) – 2(5 + (1/4))

3 (5/4)  =  3 (19/4) - 2(21/4)

(15/4)  =  (57/4) - (42/4)

(15/4)  =  (57 - 42)/4

15/4  =  15/4

Hence 1/4 is the zero of the given polynomial.

Example 2 :

Verify whether the following are roots of the polynomial equations indicated against them.

2x² - 3x - 2 = 0 ; x = 2, 3

Solution :

Let p(x)  =  2x² - 3x - 2

If x = 2

 p(2)  =  2(2)² - 3(2) - 2

  =  2(4) - 6 - 2

  =  8 - 8

p(2)  =  0

So, 2 is the zero of polynomial. 

If x = 3

 p(3)  =  2(3)² - 3(3) - 2

  =  2(9) - 9 - 2

  =  18 - 11

p(3)  =  7 ≠ 0

So, 3 is not the zero of polynomial. 

Example 3 :

Verify whether the following are roots of the polynomial equations indicated against them.

x³ - 2x² - x + 2 = 0;  x = -1, 2, 3

Solution :

Let p(x)  =  x³ - 2x² - x + 2

Instead of x, we have to apply -1.

p(-1)  =  (-1)³ - 2(-1)² - (-1) + 2

  =  -1 - 2(1) + 1 + 2

  =  -1 - 2 + 1 + 2 

  =  0

Since we get 0, -1 is the zero of the polynomial.

Now, we have to apply 2 instead of x.

p(2)  =  2³ - 2(2)² - 2 + 2

  =  8 - 2(4) - 2 + 2

  =  8 - 8 

  =  0

Since we get 0, 2 is the zero of the polynomial.

Now, we have to apply 3 instead of x.

p(3)  =  3³ - 2(3)² - 3 + 2

  =  27 - 2(9) - 3 + 2

  =  27 - 18 - 3 + 2

≠ 0

Since we do not get 0, 3 is not the zero of the polynomial.

After having gone through the stuff given above, we hope that the students would have understood, "How to Check if the Given Value is the Zero of the Polynomial"

Apart from the stuff given in "How to Check if the Given Value is the Zero of the Polynomial", if you need any other stuff in math, please use our google custom search here

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.