Question

A quadratic equation is shown below:

9x2 − 36x + 36 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 2x2 − 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used. (5 points)

Answer 1

A.
radicand or determinant is if have equation
ax^2+bx+c=0
determinant is

`b^2-4a}`
if
`b^2-4ac`>0, then you have 2 real roots
if
`b^2-4ac`=0, then you ahve 1 real root
if
`b^2-4ac`<0, then you ahve 2 complex roots

9x^2-36+36
a=9b
b=-36
c=36


`(-36)^2-4(9)(36)`

`(-36)^2-(36)(36)`
we can see that they cancel out and therefor
`b^2-4ac`=0
there is 1 real root


B. factor
(2x-7)(x-1)=0
set each to zero
2x-7=0
2x=7
x=7/2

x-1=0
x=1

x=7/2 and 1