Find the Quadratic Equation -3 , 13

$- 3$ , $13$

Step 1

$x = - 3$ and $x = 13$ are the two real distinct solutions for the quadratic equation, which means that $x + 3$ and $x - 13$ are the factors of the quadratic equation.

$(x + 3) (x - 13) = 0$

Step 2

Expand $(x + 3) (x - 13)$ using the FOIL Method.

Apply the distributive property.

$x (x - 13) + 3 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 + 3 (x - 13) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 13 + 3 x + 3 \cdot - 13 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 13 + 3 x + 3 \cdot - 13 = 0$

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

$x^{2} - 13 \cdot x + 3 x + 3 \cdot - 13 = 0$

Multiply $3$ by $- 13$ .

$x^{2} - 13 x + 3 x - 39 = 0$

Add $- 13 x$ and $3 x$ .

$x^{2} - 10 x - 39 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 3, 13}$ is $y = x^{2} - 10 x - 39$ .

$y = x^{2} - 10 x - 39$

Step 5

Find the Quadratic Equation -3 , 13

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