Find the Roots (Zeros) f(x)=5(x-2)(x^2-3x-4)

$f (x) = 5 (x - 2) (x^{2} - 3 x - 4)$

Step 1

Set $5 (x - 2) (x^{2} - 3 x - 4)$ equal to $0$ .

$5 (x - 2) (x^{2} - 3 x - 4) = 0$

Step 2

Solve for $x$ .

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

$x - 2 = 0$

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

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x^{2} - 3 x - 4$ equal to $0$ and solve for $x$ .

Set $x^{2} - 3 x - 4$ equal to $0$ .

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

Solve $x^{2} - 3 x - 4 = 0$ for $x$ .

Factor $x^{2} - 3 x - 4$ 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 $- 4$ and whose sum is $- 3$ .

$- 4, 1$

Write the factored form using these integers.

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

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

$x - 4 = 0$

$x + 1 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 4) (x + 1) = 0$ true.

$x = 4, - 1$

The final solution is all the values that make $5 (x - 2) (x^{2} - 3 x - 4) = 0$ true.

$x = 2, 4, - 1$

Step 3

Find the Roots (Zeros) f(x)=5(x-2)(x^2-3x-4)

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