Lesson: Solving Problems Involving Quadratic Equations and Rational Algebraic Equations

Activity 2. Fill Me Up Complete the table by supplying the missing steps. 1. The sum of the number and its reciprocal is -. What are the numbers? Steps Task 1.Represent the number and its a. Let x = the number reciprocal = the reciprocal of the number 2.Formulate the equation b. x+ = = 3.Multiply both sides of the equation by c. The LCD is 4x. the LCD 19 (4x) (4x) x+ = = 7 4x2 + 4 = 17x 4. Write the resulting equation in d. 4x2 - 17x -4 =0 standard form ax2+bx+c=0 5. Solve the equation in #4 by factoring e. (x-4) (4x-1)=0 6.Equate each factor to 0 (Zero Product f. Property) 7.Solve for x. g. 8.Conclusion h. The number is and its reciprocal is 2. The sum of the number and its reciprocal is 101. 70 . What are the numbers? Steps Task 1. Represent the number and its a. Let x = the number reciprocal = the reciprocal of the number 2.Formulate the equation b. 3.Multiply both sides of the equation by | c. The LCD is 10x. the LCD4.Write the resulting equation in d. 10x2-101x+10=0 standard form ax?+bx+c=0 5. Solve the equation in #4 by factoring e. (x-10) (10x-1)=0 6.Equate each factor to 0 (Zero Product f. x-10 =0, 10x-1 =0 Property) 7.Solve for x g. 8.Conclusion h. The number is and its reciprocal is 3. It takes Liza 12 hours more to disinfect their house than it takes her husband. If they work together, they can finish the same job in 8 hours. How long would it take her husband to finish the job alone? Steps Task 1. Represent the unknown in the a. Let x = the number of hours it took Liza's given problem husband to complete the job x + 12 - the number of hours it took Liza to complete the job = = part of the job done by Liza's husband in one hour x+12 part of the job done by Liza in one hour - part of the job done in one hour if they work together 2.Formulate the equation 1 b. + x+12 8 3. Multiply both sides of the equation c. The LCD is (8)(x)(x+12). by the LCD [(8)(x)(x+ 12)]+=)-()1(8)(x)(x+12)] 8x+96+8x = x2+12x 16x+96 = x2+12x 4. Write the resulting equation(step 3) d. in standard form ax2+bx+c=0 5. Solve the equation in #4 by|e. (x-12)(x+8)=0 factoring 6.Equate each factor to 0 (Zero f. x-12 =0, x +8 =0 Product Property) 7.Solve for x. g. 8/11 8.Conclusion h. Liza's husband can finish the job alone in hours. 4. Two faucets can fill a tank together in 12 minutes. Alone, it takes faucet B ten minutes less than faucet A to fill the same tank. How many minutes does it take each faucet to fill the tank separately? Steps Task 1. Represent the unknown in the given a. Let x = number of minutes it takes problem faucet A to fill the tank alone x-10 = number of minutes it takes faucet B to fill the tank alone = = part of the job done by faucet A in one minute x-10 - part of the job done by faucetB in one minute part of the job done by both faucets working together 2. Formulate an equation b. x-10 3. Multiply both sides of an equation by c. The LCD is (12)(x)(x-10). the LCD (12)(x)(x-10) += (12)(x)(x-10). 12x - 120 + 12x = x2 - 10x 4. Write the resulting equation(step 3) in d. x2-34x+120=0 standard form ax?+bx+c=0 5. Solve the equation in #4 by factoring 6.Equate each factor to 0 (Zero Product f. x-4 =0 , x-30 =0 Property) 7.Solve for x. g. 8.Conclusion h. Faucet A can fill the tank in minutes and Faucet B can fill the tank in minutes. Remember: Steps in Solving Problems Involving Quadratic Equation. 1. Read and analyze the given problem. 2. Make a representation for unknown of the problem. 3. Formulate an equation based on the conditions given in the problem. 4. Solve the value of the variable. 5. Make a conclusion. Steps in Solving Problems Involving Rational Algebraic Equation. 1. Read and analyze the given problem. 2. Make a representation for the unknown in the problem. 3. Formulate an equation based on the conditions given in the problem. 4. Transform the equation to quadratic equation in standard form. 5. Solve the equation to find the value of the variable. 6. Make a conclusion