Find the Roots (Zeros) f(x)=x^2-16x+48

$f (x) = x^{2} - 16 x + 48$

Step 1

Set $x^{2} - 16 x + 48$ equal to $0$ .

$x^{2} - 16 x + 48 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} - 16 x + 48$ 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 $48$ and whose sum is $- 16$ .

$- 12, - 4$

Write the factored form using these integers.

$(x - 12) (x - 4) = 0$

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

$x - 12 = 0$

$x - 4 = 0$

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

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

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

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.

$x = 4$

The final solution is all the values that make $(x - 12) (x - 4) = 0$ true.

$x = 12, 4$

Step 3

Find the Roots (Zeros) f(x)=x^2-16x+48

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