Write a quadratic equation having the given numbers as solutions. 4, (2)/(3)

Name: Problem 36, Chapter 11: Elementary and Intermediate Algebra
Uploaded: 2020-05-26T02:11:25-08:00
Duration: 1 min 35 s
Channel: Julie Silva
Description: Write a quadratic equation having the given numbers as solutions. 4, (2)/(3)

step 1 We're being asked to write the quadratic equations whose solutions are 4 and 2 thirds. Well, bec

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

Key Concepts

Clearing Fractions

When one or both of the given roots are fractions, it might be necessary to clear the fractions by multiplying the entire equation by an appropriate common denominator. This process simplifies the equation and results in integer coefficients, making the equation easier to work with.

Constructing a Quadratic Equation from Given Roots

To form a quadratic equation when the roots are known, you express the equation as (x - r?)(x - r?) = 0, where r? and r? represent the two solutions. Expanding this product yields the quadratic equation in the standard form.

Factor Theorem

According to the factor theorem, if r is a root of the polynomial equation, then (x - r) is a factor of the polynomial. This concept allows one to construct a quadratic equation from its roots by forming the product of the factors related to each solution.

Roots or Solutions

The solutions or roots of a quadratic equation are the values of the variable that satisfy the equation. When two numbers are provided as solutions, it implies that the quadratic can be expressed as having two linear factors corresponding to these roots.

Quadratic Equation

A quadratic equation is a second degree polynomial equation generally written in the form ax² + bx + c = 0, where a, b, and c are constants and a ? 0. This type of equation is fundamental in algebra and appears in various applications ranging from physics to economics.

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