How many roots does the following quadratic function of t have: f(t) = a + bt + ct^2 if it is known that f(t) >=0 for all values of t ?
To write more clearly, the function is;
#f(t) = a + bt + ct^2#
The function f has:
a) Exactly 2 roots
b) no roots
c) Exactly one root
d) At most one root
To write more clearly, the function is;
The function f has:
a) Exactly 2 roots
b) no roots
c) Exactly one root
d) At most one root
2 Answers
d) At most one root.
Explanation:
There are two possible conditions that satisfy the specification:
The above says that all of the points have a y value greater than 0, except, perhaps, 1 point has a y value that equals 0. The inequality does not guarantee that 1 point has a y value that is equal to 0 but it leaves it as a possibility. Therefore, the correct selection is:
d) At most one root.
At most one root
Explanation:
The graph of
Since
An upward opening parabola can intersect the
Therefore, the parabola intersects the