Find the Quadratic Equation 6 , 13

$6$ , $13$

Step 1

$x = 6$ and $x = 13$ are the two real distinct solutions for the quadratic equation, which means that $x - 6$ and $x - 13$ are the factors of the quadratic equation.

$(x - 6) (x - 13) = 0$

Step 2

Expand $(x - 6) (x - 13)$ using the FOIL Method.

Apply the distributive property.

$x (x - 13) - 6 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 - 6 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 - 6 x - 6 \cdot - 13 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 13 - 6 x - 6 \cdot - 13 = 0$

Move $- 13$ to the left of $x$ .

$x^{2} - 13 \cdot x - 6 x - 6 \cdot - 13 = 0$

Multiply $- 6$ by $- 13$ .

$x^{2} - 13 x - 6 x + 78 = 0$

Subtract $6 x$ from $- 13 x$ .

$x^{2} - 19 x + 78 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${6, 13}$ is $y = x^{2} - 19 x + 78$ .

$y = x^{2} - 19 x + 78$

Step 5

Find the Quadratic Equation 6 , 13

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