Zeroes of polynomials - HiSet: High School Equivalency Test: Math
Card 0 of 4
The equation
has two distinct solutions. What is their sum?
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.
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
If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient
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The graph of the polynomial function
has one and only one zero on the interval 
. On which subinterval is it located?
The graph of the polynomial function
has one and only one zero on the interval 
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 
.
The Intermediate Value Theorem (IVT) states that if the graph of a function 
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Which of the functions below best matches the graphed function?
Which of the functions below best matches the graphed function?
First, look at the zeroes of the graph. Zeroes are where the function touches the x-axis (i.e. values of 
where 
).
The graph shows the function touching the x-axis when 
, 
, and at a value in between 1.5 and 2.
Notice all of the possible answers are already factored. Therefore, look for one with a factor of 
(which will make 
when 
), a factor of 
to make 
when 
, and a factor which will make 
when 
is at a value between 1.5 and 2.
This function fills the criteria; it has an 
and an 
factor. Additionally, the third factor, 
, will result in 
when 
, which fits the image. It also does not have any extra zeroes that would contradict the graph.
First, look at the zeroes of the graph. Zeroes are where the function touches the x-axis (i.e. values of 
The graph shows the function touching the x-axis when 
Notice all of the possible answers are already factored. Therefore, look for one with a factor of 
This function fills the criteria; it has an 
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The graph of a function is shown below, with labels on the y-axis hidden.
Determine which of the following functions best fits the graph above.
The graph of a function is shown below, with labels on the y-axis hidden.
Determine which of the following functions best fits the graph above.
Use the zeroes of the graph to determine the matching function. Zeroes are values of x where 
. In other words, they are points on the graph where the curve touches zero.
Visually, you can see that the curve crosses the x-axis when 
, 
, and 
. Therefore, you need to look for a function that will equal zero at these x values.
A function with a factor of 
will equal zero when 
, because the factor of 
will equal zero. The matching factors for the other two zeroes, 
and 
, are 
and 
, respectively.
The answer choice 
has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of 
, which results in a zero at 
. This additional zero that isn't present in the graph indicates that this cannot be matching function.
is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are.
Use the zeroes of the graph to determine the matching function. Zeroes are values of x where 
Visually, you can see that the curve crosses the x-axis when
A function with a factor of
The answer choice
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