Write a quadratic equation having the given numbers as solutions. -(1)/(4),-(1)/(2)

Name: Problem 37, Chapter 11: Elementary and Intermediate Algebra
Uploaded: 2020-05-26T02:13:28-08:00
Duration: 1 min 39 s
Channel: Julie Silva
Description: Write a quadratic equation having the given numbers as solutions. -(1)/(4),-(1)/(2)

step 1 We're being asked to find a quadratic equation whose two solutions are negative one -fourth and

Write a quadratic equation having the given numbers as...

Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants with a ? 0. It is fundamental in algebra and appears in various problem-solving contexts such as finding the points where a quadratic function crosses the x-axis.

Roots of a Quadratic Equation

The roots (or solutions) of a quadratic equation are the values of the variable that satisfy the equation, meaning they make the equation equal to zero. These roots can be found using methods such as factoring, completing the square, or applying the quadratic formula, and they represent the x-intercepts of the function's graph.

Factored Form Representation

When the roots of a quadratic equation are known, the equation can be written in factored form as a(x - r?)(x - r?) = 0, where r? and r? are the roots and a is a non-zero constant. This form directly shows the solutions of the equation and is useful in understanding the structure and behavior of quadratic functions.

Vieta's Formulas

Vieta's formulas provide a relationship between the coefficients of a quadratic equation and its roots. For an equation in the form ax² + bx + c = 0, the sum of the roots is -b/a and the product is c/a. These relationships are helpful for constructing a quadratic equation when the roots are given, as they allow for a straightforward calculation of the coefficients.

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