? Polynomial function is nothing but combination of variables and integers. A polynomial function is defined by P(x)
Where P(x) = b n x n + b n-1 x n-1 + . . . +b2 +b1 +b0 now zeros of a polynomial function mean P (x) = 0
b n x n + b n-1 x n-1 + . . . + b2x2 + b1x + b0 = 0
If the zeros of x is real then it is called real zero and the zeros of x is imaginary mean then it is called imaginary zero.
How to Find the Zeros of a Polynomial Function:
If P (x) = b1x + b0 then zeros of the polynomial function x = -b0 / b1
P (x) = ax^2 + b x + c then zeros of a polynomial function = '(-b +- sqrt(b^2 - 4ac))/(2a)'
If the given polynomial is having a degree 1 then it is having the zeros are 1. And if it is having the degree is 2 then it is called quadratic function and it is having the zeros of a function is 2. The number of zeros of a polynomial function is depends on the degree of the polynomial function. We can find the zeros of a quadratic function using the factorization method.
Examples to Find the Zeros of a Polynomial Function:
Ex 1: Find the zeros of a following polynomial function where P (x) = x^2 + 5x +6
Sol : Given polynomial function P(x) = x^2 + 5x +6
To find the zeros of the function we have to plug P (x) = 0
So, x^2 + 5x +6 = 0
Here a = 1, b= 5 and c = 6
X = '(-5 +- sqrt(5^2 - 4 . 1 . 6))/(2 . 1)'
X = '(-5 +- sqrt(25 - 24))/(2)'
X = '(-5 +- sqrt(1))/(2)'
X = '(-5 +- 1)/(2)'
X = '(-5 + 1)/(2)', '(-5 - 1)/(2)'
X = -2 and X = -3
So zeros of the given function x = -2 and -3
Ex 2: Find the zeros of the following polynomial function P (z) = 2z + 4
Sol : Given polynomial function P (z) = 2z + 4
To find the zeros of the function P (z) = 0
So 2z + 4 = 0 Add -4 on both sides of the polynomial