Find the Quadratic Equation 14 , -3

$14$ , $- 3$

Step 1

$x = 14$ and $x = - 3$ are the two real distinct solutions for the quadratic equation, which means that $x - 14$ and $x + 3$ are the factors of the quadratic equation.

$(x - 14) (x + 3) = 0$

Step 2

Expand $(x - 14) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) - 14 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 14 (x + 3) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 3 - 14 x - 14 \cdot 3 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 - 14 x - 14 \cdot 3 = 0$

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

$x^{2} + 3 \cdot x - 14 x - 14 \cdot 3 = 0$

Multiply $- 14$ by $3$ .

$x^{2} + 3 x - 14 x - 42 = 0$

Subtract $14 x$ from $3 x$ .

$x^{2} - 11 x - 42 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${14, - 3}$ is $y = x^{2} - 11 x - 42$ .

$y = x^{2} - 11 x - 42$

Step 5

Find the Quadratic Equation 14 , -3

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