Zero of Polynomial x^2 - 5x + 6

To find the zero of the given polynomial x^2 - 5x + 6, we need to solve the equation x^2 - 5x + 6 = 0. The zeros of a polynomial are the values of x for which the polynomial evaluates to zero.

Factoring the Polynomial

One approach to finding the zeros of a quadratic polynomial is to factor it. In this case, we can factor the quadratic polynomial x^2 - 5x + 6 by finding two numbers whose product is 6 and whose sum is -5. By trial and error, we find that -2 and -3 satisfy these conditions. Therefore, we can factor the polynomial as (x - 2)(x - 3) = 0.

Setting Each Factor to Zero

To find the zeros of the polynomial, we set each factor equal to zero and solve for x.

Setting x - 2 = 0, we add 2 to both sides of the equation, giving x = 2.

Setting x - 3 = 0, we add 3 to both sides of the equation, giving x = 3.

Therefore, the zeros of the polynomial x^2 - 5x + 6 are x = 2 and x = 3.

Graphical Representation

We can also represent the zeros of the polynomial on a graph. The zeros correspond to the x-intercepts of the graph, where the polynomial crosses the x-axis.

By plotting the graph of the polynomial, we can observe that it intersects the x-axis at x = 2 and x = 3. These are the same values we obtained algebraically.

Summary

To summarize, the zero of the polynomial x^2 - 5x + 6 is x = 2 and x = 3. We found the zeros by factoring the polynomial and setting each factor equal to zero. Additionally, we visually confirmed the zeros by plotting the graph of the polynomial and observing the x-intercepts.