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Q8.

Expert-verified

Algebra 1

Found in: Page 513

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.
$\underline{x - 2 = 0}$ 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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept for quadratic equation.

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

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

Most popular questions for Math Textbooks

Which of the following numbers is less than zero?

$A 1.03 \times 10^{- 21} G 7.5 \times 10^{2} H 8.21543 \times 10^{10} J none of the above$

MULTIPLE CHOICE A rectangle has a length that is 2 inches longer than its width. The area of the rectangle is 48 square inches. What is the length of the rectangle?

F 48 in.

G 8 in.

H 6 in.

J 2 in.

Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.

$x^{2} + 12 x + 36$ .

Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.

$x^{4} - 1$

Factor each polynomial.

$x^{2} + 4 x - 21$

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