# What is the geometrical meaning of polynomial?

Solution :

In Mathematics, a polynomial is an algebraic expression which is in the form of P(x) = anxn + an-1xn-1+….+a1x1+a0, where an, an-1, a1​​​​, a0 are the real numbers, where an≠0. Also, we have learned the terms related to the polynomials, such as coefficients, terms, degree of a polynomial, zeroes of a polynomial and so on. The polynomial that involves one variable is called a polynomial in one variable. If a polynomial contains two variables, then it is called a polynomial in two variables, etc.

Coefficient:

A coefficient is a real number that is present along with variables.

Degree of a Polynomial:

The highest power of the variable of a given polynomial is called the degree of a polynomial. For example, the linear polynomial has a degree of 1, the quadratic polynomial has a degree of 2, the degree of the cubic polynomial is 3, and so on.

Zero of the Polynomial:

The zero of a polynomial P(x), when x=k is the value obtained by substituting x as “k”, where k is a real number.

It means that a real number k is the zero of a polynomial p(x) if p(k)=0.

Now, let us discuss the geometrical meaning of the zeroes of a linear polynomial  in detail.  In general, we can say that a linear polynomial ax+b, where a≠0, has exactly one zero. The zero of the linear polynomial is the x-coordinate of the point where the graph of y=ax+b intersects at the x-axis.

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