Find the Quadratic Equation Given the Roots 2 and -5

$2$ and $- 5$

$x = 2$ and $x = - 5$ are the two real distinct solutions for the quadratic equation, which means that $x - 2$ and $x + 5$ are the factors of the quadratic equation.

$(x - 2) (x + 5) = 0$

Expand $(x - 2) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) - 2 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 2 (x + 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 5 - 2 x - 2 \cdot 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $5$ .

$x^{2} + 5 x - 2 x - 10 = 0$

Subtract $2 x$ from $5 x$ .

$x^{2} + 3 x - 10 = 0$

The standard quadratic equation using the given set of solutions ${2, - 5}$ is $y = x^{2} + 3 x - 10$ .

$y = x^{2} + 3 x - 10$

Find the Quadratic Equation Given the Roots 2 and -5

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