Finding the Zeros of a Function: Methods and Techniques for Solving Math Equations

Zeros of a function f(x) is…

The zeros of a function f(x), also known as the roots or x-intercepts, are the values of x that make the function equal to zero

The zeros of a function f(x), also known as the roots or x-intercepts, are the values of x that make the function equal to zero. In other words, if you substitute these values into the function, f(x) will be equal to zero.

Mathematically, the zeros of a function f(x) can be found by solving the equation f(x) = 0. This equation represents the points on the graph where the function intersects the x-axis.

To find the zeros of a function, you can use different methods depending on the complexity of the function. Here are a few common techniques:

1. Factoring: If the function is in factored form, you can set each factor equal to zero and solve for x. For example, if the function is f(x) = (x + 2)(x – 3)(x + 1), you would set each factor (x + 2), (x – 3), and (x + 1) equal to zero and solve for x:
x + 2 = 0 –> x = -2
x – 3 = 0 –> x = 3
x + 1 = 0 –> x = -1
So, the zeros of this function are x = -2, x = 3, and x = -1.

2. Quadratic formula: If the function is quadratic in nature (in the form of ax^2 + bx + c = 0), you can use the quadratic formula to find the zeros. The quadratic formula is x = (-b ± √(b^2 – 4ac))/(2a). For example, if the function is f(x) = x^2 – 4x + 3, you would use the quadratic formula with a = 1, b = -4, and c = 3 to find the zeros:
x = (-(-4) ± √((-4)^2 – 4(1)(3)))/(2(1))
Simplifying further,
x = (4 ± √(16 – 12))/(2)
x = (4 ± √4)/(2)
x = (4 ± 2)/2
Thus, the zeros of this function are x = 1 and x = 3.

3. Graphical method: You can also find the zeros of a function by graphing it on a coordinate plane and observing the points where the graph intersects the x-axis. This can be done by plotting the function on a graphing calculator or by hand. The x-coordinate of each intersection point will correspond to a zero of the function.

It is important to note that not all functions will have real zeros. Some functions may have complex or imaginary zeros.

Remember to always verify your solutions by substituting them back into the original function to ensure they produce a value of zero.

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