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A quadratic equation is shown below: 9x2 − 16x + 60 = 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 − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer :

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9x^2 - 16x + 60
Find the discriminant, b^2 - 4ac, which is the same as the value of the radicand.
(-16)^2 - 4 * 9 * 60 = -1904
Since the discriminant is negative, there will be NO real solutions, and 2 complex solutions.

Part B.
4x^2 + 8x - 5 = 0
You can tell if a quadratic is factorable if you find the discriminant and it is a perfect square. The discriminant for this quadratic is 144 so it is factorable.
(2x + 5)(2x - 1) = 0
Set each factor equal to zero.
2x + 5 = 0                                                    2x - 1 = 0
subt 5 from both sides                                add 1 to both sides
2x = -5                                                        2x = 1
divide both sides by 2                                divide both sides by 2
x = -5/2                                                        x = 1/2

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