Find the Roots (Zeros) f(x)=x^2-5x-24

$f (x) = x^{2} - 5 x - 24$

Step 1

Set $x^{2} - 5 x - 24$ equal to $0$ .

$x^{2} - 5 x - 24 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} - 5 x - 24$ 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 $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$(x - 8) (x + 3) = 0$

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

$x - 8 = 0$

$x + 3 = 0$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $(x - 8) (x + 3) = 0$ true.

$x = 8, - 3$

Step 3

Find the Roots (Zeros) f(x)=x^2-5x-24

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