Find the Roots (Zeros) y=x^2+10x-171

$y = x^{2} + 10 x - 171$

Step 1

Set $x^{2} + 10 x - 171$ equal to $0$ .

$x^{2} + 10 x - 171 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} + 10 x - 171$ 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 $- 171$ and whose sum is $10$ .

$- 9, 19$

Write the factored form using these integers.

$(x - 9) (x + 19) = 0$

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

$x - 9 = 0$

$x + 19 = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x + 19$ equal to $0$ and solve for $x$ .

Set $x + 19$ equal to $0$ .

$x + 19 = 0$

Subtract $19$ from both sides of the equation.

$x = - 19$

The final solution is all the values that make $(x - 9) (x + 19) = 0$ true.

$x = 9, - 19$

Step 3

Find the Roots (Zeros) y=x^2+10x-171

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