Find the Equation with Real Coefficients x=2 x=4

$x = 2$ $x = 4$

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 $0$ .

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

Step 2

Simplify.

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

$x^{2} - 4 \cdot x - 2 x - 2 \cdot - 4 = 0$

Multiply $- 2$ by $- 4$ .

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

Subtract $2 x$ from $- 4 x$ .

$x^{2} - 6 x + 8 = 0$