Find the Quadratic Equation -2 , 7

$- 2$ , $7$

Step 1

$x = - 2$ and $x = 7$ are the two real distinct solutions for the quadratic equation, which means that $x + 2$ and $x - 7$ are the factors of the quadratic equation.

$(x + 2) (x - 7) = 0$

Step 2

Expand $(x + 2) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) + 2 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 2 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 2 x + 2 \cdot - 7 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 + 2 x + 2 \cdot - 7 = 0$

Move $- 7$ to the left of $x$ .

$x^{2} - 7 \cdot x + 2 x + 2 \cdot - 7 = 0$

Multiply $2$ by $- 7$ .

$x^{2} - 7 x + 2 x - 14 = 0$

Add $- 7 x$ and $2 x$ .

$x^{2} - 5 x - 14 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 2, 7}$ is $y = x^{2} - 5 x - 14$ .

$y = x^{2} - 5 x - 14$

Step 5

Find the Quadratic Equation -2 , 7

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