Math Terms from Homework 1021 LSU

Which of the following equations is not disguised quadratic equation? a. x^(2/3)-9x^(1/3)+8=0 b. x^5-x^3-6=0 c. 3x^(-2)-5x^(-1)-2=0 d. 2x^4-11x^2+12=0

b. x^5-x^3-6=0

Which of the following is true? a. All linear equations and all quadratic equations are polynomial equations. b. A polynomial equation is either a linear equation or a quadratic equation. c. Every linear equation is also a quadratic equation. d. Every quadratic equation is also a linear equation.

a. All linear equations and all quadratic equations are polynomial equations.

Which of the following statements is true? a. It is possible for an absolute value equation to have no solution. b. Every absolute value equation has two solutions. c. The solution to an absolute value equation must always be greater than or equal to zero. d. The solution to an absolute value equation is always positive.

a. It is possible for an absolute value equation to have no solution.

Which of the following statements describes the absolute value of a number a? a. The distance from the number a to 0 on a number line can be represented by the absolute value of a number a. b. The positive value of a negative number a can be represented by the absolute value of a number a. c. The opposite value of a number a can be represented by the absolute value of a number a. d. Given |a|, a is always positive.

a. The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.

Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic equation? a. There must be two real solutions. b. There must be two non real solutions. c. There will be no solutions to this quadratic equation. d. There must be exactly one real solution.

a. There must be two real solutions.

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|>c is equivalent to a. u>-c or u>c. b. u<-c or u>c. c. u<-c or u<c. d. -c<u<c.

b. u<-c or u>c.

Which of the following statements is true about rational equations?

it is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions.

Which of the following is a rational equation?

6/x -1=4/(x-2)

Which of the following statements best defines the term "algebraic expression"?

An algebraic expression consists of one or more terms that may include variables, constants, and operating symbols such as - and +.

Which of the following statements best defines the term "extraneous solution"?

An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

Which of the following best describes the zero product property?

If two factors multiplied together are equal to zero, then a least one of the factors must be zero.

Which of the following statements is true about linear equations of the form ax+b=c?

The constants a, b, and c must be real numbers with the constant a never equal to zero.

Which of the following statements best describes how to derive the quadratic formula?

The quadratic formula can be derived by solving the equation ax^2+bx+c=0, a is not = 0, for x using the method of completing the square.

Which of the following statements is not true?

The solutions to quadratic equations are always real numbers.

Which of the following statements is not true concerning the equation x^2-c=0 for c>0?

This equation is not considered to be a quadratic equation because it is not of the form ax^2+bx+c=0

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|<c is equivalent to a. u<-c or u>c. b. u<-c and u>c. c. -c<u<c. d. -c>u>c.

c. -c<u<c.

Which of the following is not a valid strategy when solving a polynomial equation of the form ax^3+bx^2=cx? a. Subtract cx from both sides. b. Set the equation equal to zero and factor out an x. c. Divide the equation by x. d. subtract ax^3 and bx^2 from both sides.

c. Divide the equation by x.

Which of the following is not a property of inequalities? a. For c>0, if a<b, ac<bc. b. For c<0, if a<b, (a/c)>(b/c) c. For c<0, if a<b, ac>bc. d. For c<0, if a<b, a-c>b-c.

d. For c<0, if a<b, a-c>b-c.

Which of the following is typically not one of the three ways to describe the solutions to a linear equality? a. Write the solution in interval notation. b. Graph the solution on a number line. c. Write the solution in set-builder notation. d. Write the solution in inequality form.

d. Write the solution in inequality form.

If u is an algebraic expression and c is a real number such that c>0, then the equation |u|=c is equivalent to a. the equation -u=c. b. the equation u=-c c. the equations u=-c and u=c. d. the equations u=-c or u=c.

d. the equations u=-c or u=c.