Find the Quadratic Equation 13 , 4

$13$ , $4$

Step 1

$x = 13$ and $x = 4$ are the two real distinct solutions for the quadratic equation, which means that $x - 13$ and $x - 4$ are the factors of the quadratic equation.

$(x - 13) (x - 4) = 0$

Step 2

Expand $(x - 13) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) - 13 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 13 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 13 x - 13 \cdot - 4 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 - 13 x - 13 \cdot - 4 = 0$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x - 13 x - 13 \cdot - 4 = 0$

Multiply $- 13$ by $- 4$ .

$x^{2} - 4 x - 13 x + 52 = 0$

Subtract $13 x$ from $- 4 x$ .

$x^{2} - 17 x + 52 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${13, 4}$ is $y = x^{2} - 17 x + 52$ .

$y = x^{2} - 17 x + 52$

Step 5

Find the Quadratic Equation 13 , 4

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