Algebra Examples

f (x) = x^{2} - 4 x + 2

$f (x) = x^{2} - 4 x + 2$

Step 1

Check the leading coefficient of the function. This number is the coefficient of the expression with the largest degree.

Largest Degree:

2

$2$

Leading Coefficient:

1

$1$

Step 2

Create a list of the coefficients of the function except the leading coefficient of

1

$1$ .

- 4, 2

$- 4, 2$

Step 3

There will be two bound options,

b_{1}

$b_{1}$ and

b_{2}

$b_{2}$ , the smaller of which is the answer. To calculate the first bound option, find the absolute value of the largest coefficient from the list of coefficients. Then add

1

$1$ .

Tap for more steps...

Step 3.1

Arrange the terms in ascending order.

b_{1} = | 2 |, | - 4 |

$b_{1} = | 2 |, | - 4 |$

Step 3.2

The maximum value is the largest value in the arranged data set.

b_{1} = | - 4 |

$b_{1} = | - 4 |$

Step 3.3

The absolute value is the distance between a number and zero. The distance between

- 4

$- 4$ and

0

$0$ is

4

$4$ .

b_{1} = 4 + 1

$b_{1} = 4 + 1$

Step 3.4

Add

4

$4$ and

1

$1$ .

b_{1} = 5

$b_{1} = 5$

b_{1} = 5

$b_{1} = 5$

Step 4

To calculate the second bound option, sum the absolute values of the coefficients from the list of coefficients. If the sum is greater than

1

$1$ , use that number. If not, use

1

$1$ .

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

The absolute value is the distance between a number and zero. The distance between

- 4

$- 4$ and

0

$0$ is

4

$4$ .

b_{2} = 4 + | 2 |

$b_{2} = 4 + | 2 |$

Step 4.1.2

The absolute value is the distance between a number and zero. The distance between

0

$0$ and

2

$2$ is

2

$2$ .

b_{2} = 4 + 2

$b_{2} = 4 + 2$

b_{2} = 4 + 2

$b_{2} = 4 + 2$

Step 4.2

Add

4

$4$ and

2

$2$ .

b_{2} = 6

$b_{2} = 6$

Step 4.3

Arrange the terms in ascending order.

b_{2} = 1, 6

$b_{2} = 1, 6$

Step 4.4

The maximum value is the largest value in the arranged data set.

b_{2} = 6

$b_{2} = 6$

b_{2} = 6

$b_{2} = 6$

Step 5

Take the smaller bound option between

b_{1} = 5

$b_{1} = 5$ and

b_{2} = 6

$b_{2} = 6$ .

Smaller Bound:

5

$5$

Step 6

Every real root on

f (x) = x^{2} - 4 x + 2

$f (x) = x^{2} - 4 x + 2$ lies between

$- 5$ and

$5$ .

$- 5$ and

$5$

Enter YOUR Problem