Find the Equation with Real Coefficients x=-3 , x=5

$x = - 3$ , $x = 5$

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 $0$ .

$(x - (- 3)) (x - 5) = 0$

Step 2

Simplify.

Expand $(x + 3) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$x (x - 5) + 3 (x - 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 3 (x - 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 3 x + 3 \cdot - 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 + 3 x + 3 \cdot - 5 = 0$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x + 3 x + 3 \cdot - 5 = 0$

Multiply $3$ by $- 5$ .

$x^{2} - 5 x + 3 x - 15 = 0$

Add $- 5 x$ and $3 x$ .

$x^{2} - 2 x - 15 = 0$