Which set of characteristics produces one unique triangle? A. Two angle measures of 60∘and one angle measure of 80∘
B. One angle measure of 10∘, one angle measure of 80∘, and one angle measure of 100∘
C. One side length of 12centimeters, one side length of 5centimeters, and one side length of 6centimeters
D. One side length of 7centimeters, one side length of 10centimeters, and one side length of 9 centimeters.

ok thats very interesting

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this

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