Find the Quadratic Equation Given the Roots -4 and -5

$- 4$ and $- 5$

$x = - 4$ and $x = - 5$ are the two real distinct solutions for the quadratic equation, which means that $x + 4$ and $x + 5$ are the factors of the quadratic equation.

$(x + 4) (x + 5) = 0$

Expand $(x + 4) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) + 4 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 4 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 4 x + 4 \cdot 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 + 4 x + 4 \cdot 5 = 0$

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

$x^{2} + 5 \cdot x + 4 x + 4 \cdot 5 = 0$

Multiply $4$ by $5$ .

$x^{2} + 5 x + 4 x + 20 = 0$

Add $5 x$ and $4 x$ .

$x^{2} + 9 x + 20 = 0$

The standard quadratic equation using the given set of solutions ${- 4, - 5}$ is $y = x^{2} + 9 x + 20$ .

$y = x^{2} + 9 x + 20$

Find the Quadratic Equation Given the Roots -4 and -5

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