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 $- 5 x$ .

$x^{2} - 7 x + 10 = 0$

The standard quadratic equation using the given set of solutions ${2, 5}$ is $y = x^{2} - 7 x + 10$ .

$y = x^{2} - 7 x + 10$

Find the Quadratic Equation Given the Roots 2 and 5

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