Find the Quadratic Equation (-2,-1)

$(- 2, - 1)$

Step 1

$x = - 2$ and $x = - 1$ are the two real distinct solutions for the quadratic equation, which means that $x + 2$ and $x + 1$ are the factors of the quadratic equation.

$(x + 2) (x + 1) = 0$

Step 2

Expand $(x + 2) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$x (x + 1) + 2 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 2 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 + 2 x + 2 \cdot 1 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 + 2 x + 2 \cdot 1 = 0$

Multiply $x$ by $1$ .

$x^{2} + x + 2 x + 2 \cdot 1 = 0$

Multiply $2$ by $1$ .

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

Add $x$ and $2 x$ .

$x^{2} + 3 x + 2 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 2, - 1}$ is $y = x^{2} + 3 x + 2$ .

$y = x^{2} + 3 x + 2$

Step 5

Find the Quadratic Equation (-2,-1)

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