Find the Quadratic Equation 12 , 3

$12$ , $3$

Step 1

$x = 12$ and $x = 3$ are the two real distinct solutions for the quadratic equation, which means that $x - 12$ and $x - 3$ are the factors of the quadratic equation.

$(x - 12) (x - 3) = 0$

Step 2

Expand $(x - 12) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$x (x - 3) - 12 (x - 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 12 (x - 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 12 x - 12 \cdot - 3 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 12 x - 12 \cdot - 3 = 0$

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x - 12 x - 12 \cdot - 3 = 0$

Multiply $- 12$ by $- 3$ .

$x^{2} - 3 x - 12 x + 36 = 0$

Subtract $12 x$ from $- 3 x$ .

$x^{2} - 15 x + 36 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${12, 3}$ is $y = x^{2} - 15 x + 36$ .

$y = x^{2} - 15 x + 36$

Step 5

Find the Quadratic Equation 12 , 3

Related Questions

Support LCMGCF.com by disabling your adblocker.