Finding Zeros of a Function: Step-by-Step Guide with Examples and Solutions

Find Zeros

In order to find the zeros of a function, we need to solve for the values of the variable that make the function equal to zero

In order to find the zeros of a function, we need to solve for the values of the variable that make the function equal to zero.

Let’s first clarify that a zero of a function is a value of the variable x for which f(x) = 0.

To find the zeros of a function, we set the function equal to zero and solve for x.

For example, consider the function f(x) = 2x^2 – 5x + 3.

To find the zeros, we set f(x) equal to zero:

0 = 2x^2 – 5x + 3

This is a quadratic equation, so we can either factor it or use the quadratic formula to find the zeros.

Let’s attempt to factor the equation:

0 = (2x – 3)(x – 1)

Setting each factor equal to zero, we get:

2x – 3 = 0 or x – 1 = 0

Solving for x in each equation, we find:

2x = 3 or x = 1

Dividing both sides of the first equation by 2, we get:

x = 3/2

So, the zeros of the function f(x) = 2x^2 – 5x + 3 are x = 1 and x = 3/2.

These are the values of x for which the function equals zero.

More Answers:

Method for Approximating Definite Integrals in Mathematics
Understanding the Mean Value Theorem for Integrals: Explaining the Relationship Between Average Value and Derivative in Calculus
Understanding the Second Fundamental Theorem of Calculus: Explained and Broken Down

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