Find Where Undefined/Discontinuous (z^2+2z-35)/(z^2-15z+50)

$\frac{z^{2} + 2 z - 35}{z^{2} - 15 z + 50}$

Step 1

Set the denominator in $\frac{z^{2} + 2 z - 35}{z^{2} - 15 z + 50}$ equal to $0$ to find where the expression is undefined.

$z^{2} - 15 z + 50 = 0$

Step 2

Solve for $z$ .

Factor $z^{2} - 15 z + 50$ 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 $50$ and whose sum is $- 15$ .

$- 10, - 5$

Write the factored form using these integers.

$(z - 10) (z - 5) = 0$

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

$z - 10 = 0$

$z - 5 = 0$

Set $z - 10$ equal to $0$ and solve for $z$ .

Set $z - 10$ equal to $0$ .

$z - 10 = 0$

Add $10$ to both sides of the equation.

$z = 10$

Set $z - 5$ equal to $0$ and solve for $z$ .

Set $z - 5$ equal to $0$ .

$z - 5 = 0$

Add $5$ to both sides of the equation.

$z = 5$

The final solution is all the values that make $(z - 10) (z - 5) = 0$ true.

$z = 10, 5$

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 $0$ .

$z = 5, z = 10$

Step 4

Find Where Undefined/Discontinuous (z^2+2z-35)/(z^2-15z+50)

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