Zeros in Graph of Polynomials

What are Zeros of Polynomials?

For a polynomial P(x), we say that x = a is the zero of the polynomial if P(a) = 0, and all such zeros of a polynomial are commonly called zeros of a polynomial. For example, consider f(x) = 3x – 12. Now, put x = 4 in the polynomial, i.e., f(4) = 3×4 – 12 = 0. Thus, x = 4 is a zero of polynomial f(x) = 3x – 12....

Zeros of Polynomial Formula

For a linear polynomial of form ax + b, its zero is given by x = -b/a....

How to Find Zero of a Polynomial?

We can find the zeros of the polynomial for various types of polynomials using various methods that are discussed below....

Factor Theorem

For the polynomial P(x), the factor theorem states that if x =a is zero of P(X) iff x – a is a factor of P(x). i.e., both the following conditions should hold true....

Relation between Zeros and Coefficient

The relation between the zeros and the coefficient of the quadratic and cubic equation is discussed below....

Forming Equation with Zeros of Polynomial

For a quadratic polynomial with zeros α and β, the quadratic polynomial is given by...

Zeros in Graph of Polynomials

In the graph of any polynomial y = f(x), real zeros are the point for which the graph intersects or touches the x-axis. (as a graph with an imaginary zero never cuts the x-axis). In other words, if there are 3 real solutions of a cubic polynomial then the graph of that cubic polynomial intersects the x-axis three times, but if there is only one real solution for some cubic polynomial then it graph only cuts the x-axis once....

Fundamental Theorem of Linear Algebra

If P(x) is a polynomial of degree “n” then P(x) will have exactly n zeros, some of which may repeat....

Sample Problems on Zeros of Polynomial

Problem 1: Given that x = 2 is a zero of P(x) = x3+2x2−5x−6. Find the other two zeroes....

Practice Problems on Zeros of Polynomial

1. Find all the zeros of the polynomial f(x) = x3 – 6x2 + 11x – 6...

FAQs on Zeros of Polynomial

What are Zeros of a Polynomial?...