How do you find the zeros of a polynomial (step by step)?

All the values of x that make the polynomial equal to zero are called zeroes of a polynomial.

Answer: To find the zeros of the polynomial, we need to solve the given polynomial by using suitable methods.

Let us proceed step by step.

Explanation:

We need to follow some basic rules to determine the zeros of a polynomial.

1. Arrange the polynomial in decreasing order of their powers.

2. In general, we find the zeros of a linear polynomial, quadratic polynomial, and cubic polynomial.

3. We need to equate the given polynomial with zero and find the value of x.

4. The maximum power of the variable, that is, the degree of the polynomial decides the total number of zeros.

Let us understand better by taking a suitable example.

Let us consider a quadratic polynomial x² - 5x + 6 = 0

Solving x² - 5x + 6 = 0 by using middle term factorization.

x² - 3x - 2x + 6 = 0

(x - 3) (x - 2) = 0

x = 2 and x = 3 are the two zeros of quadratic polynomial

Here, we got 2 zeros as the degree of the given polynomial is 2.

You can use Cuemath's Quadratic Equation Calculator to find the solutions to a quadratic equation.

Hence, to find the zeros of the polynomial we need to solve the given polynomial by using suitable methods.