Find the Equation with Real Coefficients y=-2 , y=4

$y = - 2$ , $y = 4$

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(y - (- 2)) (y - 4) = 0$

Simplify.

Expand $(y + 2) (y - 4)$ using the FOIL Method.

Apply the distributive property.

$y (y - 4) + 2 (y - 4) = 0$

Apply the distributive property.

$y \cdot y + y \cdot - 4 + 2 (y - 4) = 0$

Apply the distributive property.

$y \cdot y + y \cdot - 4 + 2 y + 2 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$y^{2} + y \cdot - 4 + 2 y + 2 \cdot - 4 = 0$

Move $- 4$ to the left of $y$ .

$y^{2} - 4 \cdot y + 2 y + 2 \cdot - 4 = 0$

Multiply $2$ by $- 4$ .

$y^{2} - 4 y + 2 y - 8 = 0$

Add $- 4 y$ and $2 y$ .

$y^{2} - 2 y - 8 = 0$