Find the zeros of the function algebraically. Give exact answers. f(x)=3 x^2+5 x+1

Name: Problem 82, Chapter 3: College Algebra: Graphs and Models
Uploaded: 2021-06-30T22:08:16-08:00
Duration: 1 min 18 s
Channel: Palitha Reddy
Description: Find the zeros of the function algebraically. Give exact answers. f(x)=3 x^2+5 x+1

step 1 So for this question, we are asked to find the zeros of the function. So pretty much what we're

Find the zeros of the function algebraically. Give exact...

Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0. It is a fundamental concept in algebra, used in various applications from physics to economics. Understanding quadratic equations involves methods of solving for the variable that make the expression equal to zero.

Zeros of a Function

The zeros of a function are the input values that make the function equal to zero. Finding the zeros of a polynomial function is equivalent to determining the points at which the graph of the function intersects the x-axis. This concept is critical in algebra, and methods for finding zeros include factoring, using the quadratic formula, and completing the square.

Quadratic Formula

The quadratic formula is a universal method for solving any quadratic equation. It states that the solutions for ax² + bx + c = 0 are given by x = (-b ± ?(b² - 4ac))/(2a). This formula is essential because it provides an exact answer for the roots of the quadratic equation, regardless of whether the roots are real or complex.

Discriminant

The discriminant, given by b² - 4ac in the quadratic formula, indicates the nature of the roots of a quadratic equation. A positive discriminant means that the equation has two distinct real roots, zero indicates one real double root, and a negative discriminant implies that the roots are complex conjugates. Understanding the discriminant is crucial for determining the type of solutions without fully solving the equation.

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