Zeroes of polynomials - HiSET

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 .

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.

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.

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.

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 .

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.

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 .

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.

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.

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.

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.

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.

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 .

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.

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.