Find the Quadratic Equation (5,40)

$(5, 40)$

Step 1

$x = 5$ and $x = 40$ are the two real distinct solutions for the quadratic equation, which means that $x - 5$ and $x - 40$ are the factors of the quadratic equation.

$(x - 5) (x - 40) = 0$

Step 2

Expand $(x - 5) (x - 40)$ using the FOIL Method.

Apply the distributive property.

$x (x - 40) - 5 (x - 40) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 40 - 5 (x - 40) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 40 - 5 x - 5 \cdot - 40 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 40 - 5 x - 5 \cdot - 40 = 0$

Move $- 40$ to the left of $x$ .

$x^{2} - 40 \cdot x - 5 x - 5 \cdot - 40 = 0$

Multiply $- 5$ by $- 40$ .

$x^{2} - 40 x - 5 x + 200 = 0$

Subtract $5 x$ from $- 40 x$ .

$x^{2} - 45 x + 200 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${5, 40}$ is $y = x^{2} - 45 x + 200$ .

$y = x^{2} - 45 x + 200$

Step 5

Find the Quadratic Equation (5,40)

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