Find the Quadratic Equation (6,-5)

$(6, - 5)$

$x = 6$ and $x = - 5$ are the two real distinct solutions for the quadratic equation, which means that $x - 6$ and $x + 5$ are the factors of the quadratic equation.

$(x - 6) (x + 5) = 0$

Expand $(x - 6) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) - 6 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 6 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 6 x - 6 \cdot 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 - 6 x - 6 \cdot 5 = 0$

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

$x^{2} + 5 \cdot x - 6 x - 6 \cdot 5 = 0$

Multiply $- 6$ by $5$ .

$x^{2} + 5 x - 6 x - 30 = 0$

Subtract $6 x$ from $5 x$ .

$x^{2} - x - 30 = 0$

The standard quadratic equation using the given set of solutions ${6, - 5}$ is $y = x^{2} - x - 30$ .

$y = x^{2} - x - 30$

Find the Quadratic Equation (6,-5)

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