Find the Quadratic Equation Given the Roots -8 and -10

$- 8$ and $- 10$

Step 1

$x = - 8$ and $x = - 10$ are the two real distinct solutions for the quadratic equation, which means that $x + 8$ and $x + 10$ are the factors of the quadratic equation.

$(x + 8) (x + 10) = 0$

Step 2

Expand $(x + 8) (x + 10)$ using the FOIL Method.

Apply the distributive property.

$x (x + 10) + 8 (x + 10) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 10 + 8 (x + 10) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 10 + 8 x + 8 \cdot 10 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 10 + 8 x + 8 \cdot 10 = 0$

Move $10$ to the left of $x$ .

$x^{2} + 10 \cdot x + 8 x + 8 \cdot 10 = 0$

Multiply $8$ by $10$ .

$x^{2} + 10 x + 8 x + 80 = 0$

Add $10 x$ and $8 x$ .

$x^{2} + 18 x + 80 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 8, - 10}$ is $y = x^{2} + 18 x + 80$ .

$y = x^{2} + 18 x + 80$

Step 5

Find the Quadratic Equation Given the Roots -8 and -10

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