Find the Roots (Zeros) f(x)=x^2-13x-30

$f (x) = x^{2} - 13 x - 30$

Step 1

Set $x^{2} - 13 x - 30$ equal to $0$ .

$x^{2} - 13 x - 30 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} - 13 x - 30$ 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 $- 30$ and whose sum is $- 13$ .

$- 15, 2$

Write the factored form using these integers.

$(x - 15) (x + 2) = 0$

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

$x - 15 = 0$

$x + 2 = 0$

Set $x - 15$ equal to $0$ and solve for $x$ .

Set $x - 15$ equal to $0$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $(x - 15) (x + 2) = 0$ true.

$x = 15, - 2$

Step 3

Find the Roots (Zeros) f(x)=x^2-13x-30

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