Find Where Undefined/Discontinuous (2z^2-288)/(z^2-9z-36)

$\frac{2 z^{2} - 288}{z^{2} - 9 z - 36}$

Step 1

Set the denominator in $\frac{2 z^{2} - 288}{z^{2} - 9 z - 36}$ equal to $0$ to find where the expression is undefined.

$z^{2} - 9 z - 36 = 0$

Step 2

Solve for $z$ .

Factor $z^{2} - 9 z - 36$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 36$ and whose sum is $- 9$ .

$- 12, 3$

Write the factored form using these integers.

$(z - 12) (z + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$z - 12 = 0$

$z + 3 = 0$

Set $z - 12$ equal to $0$ and solve for $z$ .

Set $z - 12$ equal to $0$ .

$z - 12 = 0$

Add $12$ to both sides of the equation.

$z = 12$

Set $z + 3$ equal to $0$ and solve for $z$ .

Set $z + 3$ equal to $0$ .

$z + 3 = 0$

Subtract $3$ from both sides of the equation.

$z = - 3$

The final solution is all the values that make $(z - 12) (z + 3) = 0$ true.

$z = 12, - 3$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$z = - 3, z = 12$

Step 4

Find Where Undefined/Discontinuous (2z^2-288)/(z^2-9z-36)

Related Questions

Support LCMGCF.com by disabling your adblocker.