Let's suppose that we have polynomial consisting of single variable . Zero of this polynomial can be defined as number c such that P(c)=0.
Let's take an example of a linear polynomial .
To find its zero, we will equate this polynomial to 0.
Therefore, at , we have . In other words, we can say that .
It means that is the zero of polynomial .
What is the zero of constant polynomial?
Constant polynomial does not have any zero. This is because any constant c can be written as . We cannot have any value of which will make . Value of always remain equal to c after putting any value for .
We covered one example of linear polynomial. Let's do one example of quadratic polynomial. Let' suppose that we have quadratic polynomial .
By definition of zero of the polynomial, it is the number c such that . So, we equate to find its zeros.
This is a quadratic equation. We can solve quadratic equations by factorization, completing square and by using quadratic formula. According to my view, quadratic formula is easiest to understand. So, we will solve this by using quadratic formula.
By quadratic formula:
Comparing given equation with the general quadratic equation , we get
Putting values of a, b and c in quadratic formula we get:
It means that -1 and -3 are the zeros of polynomial
In the later articles, we will learn how to find zeros of cubic and quartic polynomials.