A quadratic equation is shown below:16x2 − 8x + 1 = 0Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)Part B: Solve 4x2 − 8x − 45 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Accepted Solution
A:
16x^2 − 8x + 1 = 0
Part A: b^2 - 4ac for ax^2 + bx + c
16x^2 − 8x + 1 = 0 so in this case, a = 16, b = -8, c = 1
b^2 - 4ac =(-8)^2 - (4 * 16* 1) = 64 - 64 = 0 because it's equal 0, answer is one solution
Part B:
4x^2 − 8x − 45 = 0 solve the equation by factoring = (2x - 9)(2x + 5)
set (2x - 9)(2x + 5) equal to 0 to solve for x so (2x - 9)(2x + 5) = 0 2x - 9 = 0 x = 9/2 x = 4.5
2x + 5 = 0 x = -5/2 x = -2.5 answer x = -2.5 or x = 4.5