Final Exam 583
- Figure FE-15 shows the graphs of a linear function and a quadratic function in real-
number rectangular coordinates. The origin (0, 0) is where the x and y axes intersect.
The graphs intersect at two points. Suppose we consider these two functions as a
system. Based on the information shown,
(a) there are two solutions; both are ordered pairs of real numbers.
(b) there is a single solution with multiplicity 2; it is an ordered pair of reals.
(c) there is a single solution with multiplicity 2; it is an ordered pair of complex
numbers.
(d) there are two solutions; one is an ordered pair of reals, and the other is an ordered
pair of pure imaginary numbers.
(e) there are two solutions; one is an ordered pair of reals, and the other is an ordered
pair of complex (but not real) numbers.
- Figure FE-16 shows the graphs of two quadratic functions in real-number rectangular
coordinates. The origin (0, 0) is where the x and y axes intersect. The functions are
f (x)=a 1 x^2 +b 1 x+c 1
and
g (x)=a 2 x^2 +b 2 x+c 2
where all the coefficients and constants are real numbers, and a 1 and a 2 are both non-
zero. The graphs intersect at a single point. How can we change this system into one that
we can be certain has no real solutions?
(a) We need more information to answer this.
(b) We can decrease the value of c 1 , leaving everything else the same.
x
y
Figure FE-15 Illustration for Final Exam
Question 144.
