Find the Quadratic Equation (2,25)

$(2, 25)$

Step 1

$x = 2$ and $x = 25$ are the two real distinct solutions for the quadratic equation, which means that $x - 2$ and $x - 25$ are the factors of the quadratic equation.

$(x - 2) (x - 25) = 0$

Step 2

Expand $(x - 2) (x - 25)$ using the FOIL Method.

Apply the distributive property.

$x (x - 25) - 2 (x - 25) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 25 - 2 (x - 25) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 25 - 2 x - 2 \cdot - 25 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 25 - 2 x - 2 \cdot - 25 = 0$

Move $- 25$ to the left of $x$ .

$x^{2} - 25 \cdot x - 2 x - 2 \cdot - 25 = 0$

Multiply $- 2$ by $- 25$ .

$x^{2} - 25 x - 2 x + 50 = 0$

Subtract $2 x$ from $- 25 x$ .

$x^{2} - 27 x + 50 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${2, 25}$ is $y = x^{2} - 27 x + 50$ .

$y = x^{2} - 27 x + 50$

Step 5

Find the Quadratic Equation (2,25)

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