Question

A quadratic equation is shown below:

16x2 − 8x + 1 = 0

Part 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)

Answer 1

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

Hope it helps