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Expert-verified Found in: Page 513 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence. $\underset{\mathbf{¯}}{\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{=}\mathbf{0}}$ is a quadratic equation.

The statement is false.$a{x}^{2}+x-2=0$is a quadratic equation.

See the step by step solution

## Step 1. State the concept for quadratic equation.

A quadratic equation is a second order equation written as$a{x}^{2}+bx+c=0$where a, b, and c are coefficients of real numbers and$a\ne 0$.

A quadratic equation generally has two roots, which can be equal to each other. Some quadratic expressions can be factored, which means that the equation can be written as:

$a\left(x-{x}_{1}\right)\left(x-{x}_{2}\right)=0$

where${x}_{1}$and${x}_{1}$are the two roots of the equation.

## Step 2. State the concept for linear equation.

The given equation is in the form of$\left(x-a\right)=0$, where a is the root or the solution of the equation. The equation is a simple linear equation which has order equal to 1. That means highest power of the variable x is 1.

## Step 3. Compare the equation.

Referring to the given equation, it does not match with the above equation.

Therefore, the statement is false.

If there is addition of the term$a{x}^{2}$in the given equation then it will become a quadratic equation ### Want to see more solutions like these? 