Find the Roots (Zeros) y=2x^2+9x-11

$y = 2 x^{2} + 9 x - 11$

Step 1

Set $2 x^{2} + 9 x - 11$ equal to $0$ .

$2 x^{2} + 9 x - 11 = 0$

Step 2

Solve for $x$ .

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 11 = - 22$ and whose sum is $b = 9$ .

Factor $9$ out of $9 x$ .

$2 x^{2} + 9 (x) - 11 = 0$

Rewrite $9$ as $- 2$ plus $11$

$2 x^{2} + (- 2 + 11) x - 11 = 0$

Apply the distributive property.

$2 x^{2} - 2 x + 11 x - 11 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 2 x) + 11 x - 11 = 0$

Factor out the greatest common factor (GCF) from each group.

$2 x (x - 1) + 11 (x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$(x - 1) (2 x + 11) = 0$

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

$x - 1 = 0$

$2 x + 11 = 0$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Set $2 x + 11$ equal to $0$ and solve for $x$ .

Set $2 x + 11$ equal to $0$ .

$2 x + 11 = 0$

Solve $2 x + 11 = 0$ for $x$ .

Subtract $11$ from both sides of the equation.

$2 x = - 11$

Divide each term in $2 x = - 11$ by $2$ and simplify.

Divide each term in $2 x = - 11$ by $2$ .

$\frac{2 x}{2} = \frac{- 11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 11}{2}$

Divide $x$ by $1$ .

$x = \frac{- 11}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{2}$

The final solution is all the values that make $(x - 1) (2 x + 11) = 0$ true.

$x = 1, - \frac{11}{2}$

Step 3

Find the Roots (Zeros) y=2x^2+9x-11

Related Questions

Support LCMGCF.com by disabling your adblocker.