Which of the following is a root of the polynomial shown below fxx3x29x 9


The polynomial is shown below


The polynomial shown below has a root of 3.

f(x) = x^3 + 2x^9 + 9

This can be seen by factoring the polynomial as follows:

f(x) = (x-3)(x^2+3x+3)(x^6-3x^3+9)

Since (x-3) is a factor, that means that x=3 is a root of the polynomial.

f(x) = 3x^2 + 9x + 2

There are three roots to this polynomial equation: -1, 2, and -2.

The roots of the polynomial

The roots of the polynomial f(x) = 3x^2 – 9 are -3 and 3.

How to find the roots of the polynomial

There are a few different methods that can be used to find the roots of the polynomial f(x) = 3x^2 – 9x + 9.

One method is to factor the polynomial. In this case, the polynomial can be factored as (3x – 9)(x – 1). This means that the roots of the polynomial are -3 and 1.

Another method is to use the Quadratic Formula. The Quadratic Formula can be used to find the roots of any quadratic equation, and in this case we have a quadratic equation with coefficients a = 3, b = -9, and c = 9. Plugging these values into the Quadratic Formula, we get that the roots of the polynomial are 1/3 and 3.

Lastly, we could use synthetic division to find the roots of the polynomial. Synthetic division is a method for finding the zeros of a polynomial by dividing it by a linear factor. In this case, we would divide by (x – 1) to get that the roots are 1 and -3.

The factors of the polynomial

The factors of the polynomial are (x-3), (x-9), and (x+9).

The zeros of the polynomial

The zeros of the polynomial are its roots. The roots of the polynomial shown below are 3, -3, and -9.


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