Find the Discriminant 2y^2+4y+2=0

$2 y^{2} + 4 y + 2 = 0$

Step 1

Solve the equation for $y$ .

Factor the left side of the equation.

Factor $2$ out of $2 y^{2} + 4 y + 2$ .

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

$2 (y^{2}) + 4 y + 2 = 0$

Factor $2$ out of $4 y$ .

$2 (y^{2}) + 2 (2 y) + 2 = 0$

Factor $2$ out of $2$ .

$2 (y^{2}) + 2 (2 y) + 2 (1) = 0$

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

$2 (y^{2} + 2 y) + 2 (1) = 0$

Factor $2$ out of $2 (y^{2} + 2 y) + 2 (1)$ .

$2 (y^{2} + 2 y + 1) = 0$

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$2 (y^{2} + 2 y + 1^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 y = 2 \cdot y \cdot 1$

Rewrite the polynomial.

$2 (y^{2} + 2 \cdot y \cdot 1 + 1^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 1$ .

$2 {(y + 1)}^{2} = 0$

Divide each term in $2 {(y + 1)}^{2} = 0$ by $2$ and simplify.

Divide each term in $2 {(y + 1)}^{2} = 0$ by $2$ .

$\frac{2 {(y + 1)}^{2}}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(y + 1)}^{2}}{2} = \frac{0}{2}$

Divide ${(y + 1)}^{2}$ by $1$ .

${(y + 1)}^{2} = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

${(y + 1)}^{2} = 0$

Set the $y + 1$ equal to $0$ .

$y + 1 = 0$

Subtract $1$ from both sides of the equation.

$y = - 1$

Step 2

Since $- 1 \neq 0$ , there are no solutions.

No solution