Question

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.

Short answer

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

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:

$a(x-x_1)(x-x_2)=0$

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$(x-a)=0$, where ais 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 xis 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