Find the Quadratic Equation (3,7)

$(3, 7)$

Step 1

$x = 3$ and $x = 7$ are the two real distinct solutions for the quadratic equation, which means that $x - 3$ and $x - 7$ are the factors of the quadratic equation.

$(x - 3) (x - 7) = 0$

Step 2

Expand $(x - 3) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) - 3 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 3 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 - 3 x - 3 \cdot - 7 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 - 3 x - 3 \cdot - 7 = 0$

Move $- 7$ to the left of $x$ .

$x^{2} - 7 \cdot x - 3 x - 3 \cdot - 7 = 0$

Multiply $- 3$ by $- 7$ .

$x^{2} - 7 x - 3 x + 21 = 0$

Subtract $3 x$ from $- 7 x$ .

$x^{2} - 10 x + 21 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${3, 7}$ is $y = x^{2} - 10 x + 21$ .

$y = x^{2} - 10 x + 21$

Step 5

Find the Quadratic Equation (3,7)

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