Find the Roots (Zeros) f(x)=2x^2+10x+12

$f (x) = 2 x^{2} + 10 x + 12$

Step 1

Set $2 x^{2} + 10 x + 12$ equal to $0$ .

$2 x^{2} + 10 x + 12 = 0$

Step 2

Solve for $x$ .

Factor the left side of the equation.

Factor $2$ out of $2 x^{2} + 10 x + 12$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) + 10 x + 12 = 0$

Factor $2$ out of $10 x$ .

$2 (x^{2}) + 2 (5 x) + 12 = 0$

Factor $2$ out of $12$ .

$2 x^{2} + 2 (5 x) + 2 \cdot 6 = 0$

Factor $2$ out of $2 x^{2} + 2 (5 x)$ .

$2 (x^{2} + 5 x) + 2 \cdot 6 = 0$

Factor $2$ out of $2 (x^{2} + 5 x) + 2 \cdot 6$ .

$2 (x^{2} + 5 x + 6) = 0$

Factor.

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$2 ((x + 2) (x + 3)) = 0$

Remove unnecessary parentheses.

$2 (x + 2) (x + 3) = 0$

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

$x + 2 = 0$

$x + 3 = 0$

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.

$x = - 2$

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 $2 (x + 2) (x + 3) = 0$ true.

$x = - 2, - 3$

Step 3

Find the Roots (Zeros) f(x)=2x^2+10x+12

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