Find the Roots (Zeros) h(w)=w^2+13w+42

$h (w) = w^{2} + 13 w + 42$

Step 1

Set $w^{2} + 13 w + 42$ equal to $0$ .

$w^{2} + 13 w + 42 = 0$

Step 2

Solve for $x$ .

Factor $w^{2} + 13 w + 42$ 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 $42$ and whose sum is $13$ .

$6, 7$

Write the factored form using these integers.

$(w + 6) (w + 7) = 0$

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

$w + 6 = 0$

$w + 7 = 0$

Set $w + 6$ equal to $0$ and solve for $w$ .

Set $w + 6$ equal to $0$ .

$w + 6 = 0$

Subtract $6$ from both sides of the equation.

$w = - 6$

Set $w + 7$ equal to $0$ and solve for $w$ .

Set $w + 7$ equal to $0$ .

$w + 7 = 0$

Subtract $7$ from both sides of the equation.

$w = - 7$

The final solution is all the values that make $(w + 6) (w + 7) = 0$ true.

$w = - 6, - 7$

Step 3

Find the Roots (Zeros) h(w)=w^2+13w+42

Related Questions

Support LCMGCF.com by disabling your adblocker.