How many real solutions exist for this system of equations?
y = x2 + 4
y = 4x
A. zero
B. one
C. two
D. infinite
How many real solutions exist for this system of equations?
y = x2 + 4
y = 4x
A. zero
B. one
C. two
D. infinite
Assuming that x2 means x2....
Since they both equal y, we can set x2 + 4 = 4x
Subtracting 4x from boths sides we get x2 - 4x + 4 = 0
This is a quadratic which will factor to (x - 2)(x - 2) = 0
Now here's where language gets tricky.
A quadratic has two solutions, but in this case both solutions are x = 2.
So, is that considered one solution or two? I'd say one, because the curve touches zero at only one point, but semantics might determine what it is supposed to be called. I don't know if mathematics has a conventional nomenclature for this.
.
