Problems 112-121 are based on material learned earlier in...

Problems 112-121 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find the real zeros of $f(x)=3 x^{2}-10 x+5$

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Key Concepts

Quadratic Functions

A quadratic function is a polynomial of degree two, typically written in the form ax² + bx + c, where a, b, and c are constants with a not equal to zero. This form represents a parabola on a graph and is fundamental in many areas of algebra and calculus for modeling various phenomena.

Real Zeros

Real zeros, or roots, of a function are the values of x for which the function evaluates to zero. In the context of quadratic functions, these correspond to the x-intercepts of the parabola, providing critical information about the behavior and solution set of the equation.

Quadratic Formula

The quadratic formula is a universal method for finding the zeros of any quadratic function. It is derived from the process of completing the square and provides the solutions by substituting the coefficients a, b, and c into the formula x = (-b ± ?(b² - 4ac)) / (2a), which is particularly useful when factoring is difficult.

Discriminant

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if the discriminant is positive, there are two distinct real roots; if it is zero, there is exactly one real root (a repeated root); and if it is negative, the equation has two complex roots, indicating that there are no real zeros.

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