Finite Math Examples

y = x^{2} - 3 x - 4

$y = x^{2} - 3 x - 4$

Step 1

Set

x^{2} - 3 x - 4

$x^{2} - 3 x - 4$ equal to

0

$0$ .

x^{2} - 3 x - 4 = 0

$x^{2} - 3 x - 4 = 0$

Step 2

Solve for

x

$x$ .

Tap for more steps...

Step 2.1

Factor

x^{2} - 3 x - 4

$x^{2} - 3 x - 4$ using the AC method.

Tap for more steps...

Step 2.1.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 4

$- 4$ and whose sum is

- 3

$- 3$ .

- 4, 1

$- 4, 1$

Step 2.1.2

Write the factored form using these integers.

(x - 4) (x + 1) = 0

$(x - 4) (x + 1) = 0$

(x - 4) (x + 1) = 0

$(x - 4) (x + 1) = 0$

Step 2.2

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x - 4 = 0

$x - 4 = 0$

x + 1 = 0

$x + 1 = 0$

Step 2.3

Set

x - 4

$x - 4$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 2.3.1

Set

x - 4

$x - 4$ equal to

0

$0$ .

x - 4 = 0

$x - 4 = 0$

Step 2.3.2

Add

4

$4$ to both sides of the equation.

x = 4

$x = 4$

x = 4

$x = 4$

Step 2.4

Set

x + 1

$x + 1$ equal to

0

$0$ and solve for

x

$x$ .

Tap for more steps...

Step 2.4.1

Set

x + 1

$x + 1$ equal to

0

$0$ .

x + 1 = 0

$x + 1 = 0$

Step 2.4.2

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 2.5

The final solution is all the values that make

(x - 4) (x + 1) = 0

$(x - 4) (x + 1) = 0$ true. The multiplicity of a root is the number of times the root appears.

x = 4

$x = 4$ (Multiplicity of

1

$1$ )

x = - 1

$x = - 1$ (Multiplicity of

1

$1$ )

x = 4

$x = 4$ (Multiplicity of

1

$1$ )

x = - 1

$x = - 1$ (Multiplicity of

1

$1$ )

Step 3

Enter YOUR Problem