Find the Equation with Real Coefficients y=6 , y=4

$y = 6$ , $y = 4$

Step 1

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 $0$ .

$(y - 6) (y - 4) = 0$

Step 2

Simplify.

Expand $(y - 6) (y - 4)$ using the FOIL Method.

Apply the distributive property.

$y (y - 4) - 6 (y - 4) = 0$

Apply the distributive property.

$y \cdot y + y \cdot - 4 - 6 (y - 4) = 0$

Apply the distributive property.

$y \cdot y + y \cdot - 4 - 6 y - 6 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$y^{2} + y \cdot - 4 - 6 y - 6 \cdot - 4 = 0$

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

$y^{2} - 4 \cdot y - 6 y - 6 \cdot - 4 = 0$

Multiply $- 6$ by $- 4$ .

$y^{2} - 4 y - 6 y + 24 = 0$

Subtract $6 y$ from $- 4 y$ .

$y^{2} - 10 y + 24 = 0$