Equations That Become Quadratic

​Equations That Become Quadratic

​Objective:

​ 1. Solve equations transformable to quadratic equations

​ (including rational and algebraic equations).

 ​

​Take note of the following:

​> The solutions of rational equations that are transformable into quadratic equations can be determined using the CRAM method and the different methods of solving quadratic equations.

​

> Equations that are quadratic in form or reducible to quadratic equations can be solved using any appropriate method in solving quadratic equations.

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​The CRAM Method

​C - Clear all fractions by multiplying both sides of the equation in one variable by the LCD.​

​R - Remove all grouping symbols, if necessary.

​A - Add or subtract similar terms.

​M - Multiply or divide both sides by the numerical coefficient of the variable, leaving the variable on the LHS of the equation with a coefficient equal to 1. Then, verify or check if the values of the variable satisfy the given equation.​

​Brain Break:

https://www.youtube.com/watch?v=a9maEYcehyE​

Multiple Choice

True or False.

The LCD of the equation $$\frac{x}{x\ -\ 1}-\frac{3}{x}=\ 6$$  is x(x - 1).

• True

• False

Multiple Choice

What is the LCD of the equation $$\frac{2}{\left(3x\ +\ 2\right)^2}\ +\ \frac{1}{3x\ +\ 2}\ -\ 3\ =\ 0$$  ?

• 3x + 2

• (3x + 2)²

• (3x + 2)(3x + 2)²

• 3(3x + 2)

Multiple Choice

Find the solution set of $$\frac{1}{x}+\frac{6}{2x}=\ x$$  

• $$\pm7$$  

• $$\pm5$$  

• $$\pm4$$  

• $$\pm2$$  

​Worktext Reference

Oronce O.A., Mendoza M.O. (2019). E-Math Worktext in Mathematics 9, Manila, Philippines: REX Bookstore Inc.

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Reference:

​

Albay E.M., Oli M.C. (2018). Practical Math 9, Makati City, Philippines: Diwa Learning Systems Inc.

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