Q8. - Algebra 1

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.

Step-by-Step Solution

Answer

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

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 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