College Algebra & Trigonometry, 2018a

48 CHAPTER 1. ALGEBRA REVIEW
When we added and subtracted the square root of 24 to 6 in the quadratic formula,
this created two answers, and they were real-valued because the square
root of 24 is real-valued.
Another way to see this is graphically. If we graph y = x 2 − 6x +3and find the x
values that make y =0, these will appear along the x-axis, and will be the same
values that solve the equation x 2 − 6x +3=0.
10
5
x ≈ 0.551 x ≈ 5.449
2 4 6
−5
If we consider a related, but slightly different equation to start with, these relationships
between the roots, the discriminant and the graphical intersections will
be slightly different.
x 2 − 6x +9=0
a =1,b= −6,c=9