Question

PLEASE HELP !!

A quadratic equation is shown below:

9x^2 - 16x + 60 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work.

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.

Part C: Solve 2x2 -12x + 5 = 0 by using a method different from the one you used in Part B. Show the steps of your work.

Answer 1

9x^2 - 16x + 60 = 0

comparing it with ax^2 + bx + c = 0

a = 9 b=-16 c=60

b^2 => 256 < 2160 = 4*9*60

Hence the Equation has Complex Roots.

4x2 + 8x - 5 = 0

a = 4 b = 8 c = -5

b^2 = 64 > -80 <= 4*4*-5 Hence Real Roots Exist.

sum of Roots (p+q): -2 Product (pq): -5/4
(p-q)2 = (p+q)2 - 4pq

p-q = root (4+5) => 3 or -3
p+q = -2

=> p=1/2 (+3) or -5/2 (-3)
=> q=-5/2 (+3) or 1/2 (-3)

Roots are 1/2 , -5/2

2x2 -12x + 5 = 0

a = 2 b = -12 c = 5

b2 = 144 > 40 <= 4*2*5 Hence Real Roots Exist

The Roots are:

-b +/- root(b2-4ac)/2a

=> 12 +/- root(104)/4

=> 12 +/- 2root(26)/4

=> 6+root(26)/2 or 6-root(26)/2

Hope its Correct...