:
The credit union offered Zach a $200,000, 10 year loan at a 3.625% APR. The bank offers Zach the option to purchase points at a cost of 1% of the loan amount. Each point purchased lowers the APR by 0.125%
Part A
About how many years will it take Zach to break-even if he purchases 1 point? years
Part B
Should Zach purchase the points?

£56

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0