What does it mean zeroes of polynomial?What does it mean zeroes of polynomial?

Expert Answers
hala718 eNotes educator| Certified Educator
Let P(x)= ax^n + bx^n-1 + cx^n-2 .... + k be a polynomial. Then, the zeros of the polynomial are all x values such that P(x) = 0. In other words, if x1 is a zero of P(x), Then P(x1) = 0. I will give you an example. Let P(x) = x^2 -4x - 12 We need to find the zeros of P(x). Let us factor. ==> P(x) = (x-6)(x+2) ==> The zeros are 6 and -2. Let us verify If x= 6 is a zero for P(x) , then P(6) = 0 ==> P(6) = 6^2 - 4*6 -12 = 36 -24-12 = 36-36 = 0 ==> P(-2) = -2^2 +2*4 -12 = 4 +8 -12 = 12-12=0 Then, the zeros are 6 and -2.
pohnpei397 eNotes educator| Certified Educator

The zeroes of a polynomial are simply those values of the variables where the polynomial as a whole equals zero.

So, in other words, to find the zeroes of a polynomial, you have to set the whole polynomial equal to zero and then solve for the variable.

For example, if
x^2 - 14x + 49 = 0, you solve for x to find the zero of this polynomial.  In this case, the zero is x = 7

litteacher8 eNotes educator| Certified Educator

The zeros are the roots, or where the polynomial croses the axis.  A polynomial will have 2 roots, that means it has 2 zeros.  To find the roots you can graph and look where it crosses the axis, or you can use the quadratic equation.  This is also known as the solution.

ceenymeeny | Student

The zeroes of a polynomial are the roots of the polynomial.

The roots or the solutions of a polynomial are those values of x that cancels the polynomial.

These values of x could be real or imaginary numbers.

We'll solve an example to emphasize the idea of the root of a polynomial.

P(x) = x^2 - 6x + 5

The roots of the quadratic polynomial are 1 and 5.

We'll substitute x by 1 in the expression of P(x):

P(1) = 1^2 - 6*1 + 5

P(1) = 1-6+5

P(1) = -5+5 = 0

So, the root 1 cancels the polynomial and represents the 1st zero of P(x).

P(5) = 25 - 30 + 5 = 25-25 = 0

So, the root 5 cancels the polynomial and represents the 2nd zero of P(x).

find zero of 3x^3 - 2x^2 - x + 4

ceenymeeny | Student

The zeroes of a polynomial are the roots of the polynomial.

The roots or the solutions of a polynomial are those values of x that cancels the polynomial.

These values of x could be real or imaginary numbers.

We'll solve an example to emphasize the idea of the root of a polynomial.

P(x) = x^2 - 6x + 5

The roots of the quadratic polynomial are 1 and 5.

We'll substitute x by 1 in the expression of P(x):

P(1) = 1^2 - 6*1 + 5

P(1) = 1-6+5

P(1) = -5+5 = 0

So, the root 1 cancels the polynomial and represents the 1st zero of P(x).

P(5) = 25 - 30 + 5 = 25-25 = 0

So, the root 5 cancels the polynomial and represents the 2nd zero of P(x).

this is for quadratic polynomial.

will it be the same for cubic?

pls can u give example

 

giorgiana1976 | Student

The zeroes of a polynomial are the roots of the polynomial.

The roots or the solutions of a polynomial are those values of x that cancels the polynomial.

These values of x could be real or imaginary numbers.

We'll solve an example to emphasize the idea of the root of a polynomial.

P(x) = x^2 - 6x + 5

The roots of the quadratic polynomial are 1 and 5.

We'll substitute x by 1 in the expression of P(x):

P(1) = 1^2 - 6*1 + 5

P(1) = 1-6+5

P(1) = -5+5 = 0

So, the root 1 cancels the polynomial and represents the 1st zero of P(x).

P(5) = 25 - 30 + 5 = 25-25 = 0

So, the root 5 cancels the polynomial and represents the 2nd zero of P(x).