Lesson: Solving Problems Involving Quadratic Equations and Rational Algebraic Equations

Activities: Activity 1. Complete Me Complete the table by supplying the missing steps. Problem Steps 1. The sum of two numbers is 22 and the | a. Representation: product is 120. What are the numbers? Let x = first number 22-x = second number b. Equation: c. Solution: 22x - x2 = 120 x2 - 22x + 120 = 0 (x - 10) (x - 12) = 0 x - 10 = 0, x - 12 = 0 X = X = d. Therefore, the two numbers are and 2. The sum of two numbers is 24 and the a. Representation: product is 135. What are the numbers? Let x = first number = second number b. Equation: (x) (24 - x) = 135 c. Solution: 24x - x2 = 135 x2 - 24x + 135 = 0 (x - 15) (x - 9) = 0 x - 15 = 0, x - 9 =0 x X d. Therefore, the two numbers are and 3. The product of two consecutive a. Representation positive integers is 420. What are the Let x = first integer integers? x + 1 = second integer b. Equation: c. Solution: xz + x = 420 x2 + x - 420 = 0 (x+ 21)(x - 20) = 0 =0, =0 x = -21 , x = 20 d. Therefore, the two consecutive positive integers are and 4. The product of two consecutive a. Representation positive integers is 272. What are the Let x = first integer integers? = second integer b. Equation: x(x + 1) = 272 c. Solution: x2 + x = 272 x2 + x - 272 = 0 (x - 16)(x + 17) = 0 =0 =0x =16, x =-17 d. Therefore, the two consecutive positive integers are and 5. The length of a rectangular field is 7 a. Representation meters longer than its width and the Let x = width of the rectangular field area is 30 square meters. How wide is x+7= length of the rectangular field the garden? b. Equation: c. Solution : x + 7x = 30 x2 +7x - 30 = 0 (x + 10)(x - 3) = 0 x + 10 =0, x-3 =0 X d. The width of the garden is