Find the Quadratic Equation (-4,5)

$(- 4, 5)$

Step 1

$x = - 4$ 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.

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

Step 2

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.

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

Step 3

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 $4 x$ .

$x^{2} - x - 20 = 0$

Step 4

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

$y = x^{2} - x - 20$

Step 5

Find the Quadratic Equation (-4,5)

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