All HiSET: Math Resources
Example Questions
Example Question #1 : Identification
The equation
has two distinct solutions. What is their sum?
It is not necessary to actually find the solutions to a quadratic equation to determine the sum of its solutions.
First, get the equation in standard form by subtracting
from both sides:
If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient . In this problem,
, making
the correct choice.
Example Question #271 : Hi Set: High School Equivalency Test: Math
The graph of the polynomial function
has one and only one zero on the interval . On which subinterval is it located?
The Intermediate Value Theorem (IVT) states that if the graph of a function is continuous on an interval
, and
and
differ in sign, then
has a zero on
. Consequently, the way to answer this question is to determine the signs of
on the endpoints of the subintervals -
. We can do this by substituting each value for
as follows:
assumes positive values for
and negative values for
. By the IVT,
has a zero on
.
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