Question

A quadratic equation is shown below: x2 + 5x + 4 = 0 Part A: Describe the solution(s) to the equation by just determining radicand. Show your work. (3 points) Part B: Solve 4x2 -12x + 5 = 0 using an appropriate method. Show the steps of your work, and explain why you chose the method used. (4 points) Part C: Solve 2x2 -10x + 3 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Answer 1

Part A
x² + 5x + 4 = 0
x = -(5) +/- √((5)² - 4(1)(4))
2(1)
x = -5 +/- √(25 - 16)
2
x = -5 +/- √(9)
2
x = -5 +/- 3
2
x = -5 + 3 U x = -5 - 3
2 2
x = -2 x = -8
2 2
x = -1 x = -4

Part B
4x² - 12x + 5 = 0
x = -(-12) +/- √((-12)² - 4(4)(5))
2(4)
x = 12 +/- √(144 - 80)
8
x = 12 +/- √(64)
8
x = 12 +/- 8
8
x = 3 +/- 2
2
x = 3 + 2 U x = 3 - 2
2 2
x = 5 x = 1
2 2
x = 2.5 x = 0.5

Part C
2x² - 10x + 3 = 0
x = -(-10) +/- √((-10)² - 4(2)(3))
2(2)
x = 10 +/- √(100 - 24)
4
x = 10 +/- √(76)
4
x = 10 +/- 2√(19)
4
x = 5 +/- √(19)
2
x = 2.5 + 0.5√(19)
x = 2.5 + 0.5√(19) U x = 2.5 - 0.5√(19)