Find the Quadratic Equation -7 , 11

$- 7$ , $11$

Step 1

$x = - 7$ and $x = 11$ are the two real distinct solutions for the quadratic equation, which means that $x + 7$ and $x - 11$ are the factors of the quadratic equation.

$(x + 7) (x - 11) = 0$

Step 2

Expand $(x + 7) (x - 11)$ using the FOIL Method.

Apply the distributive property.

$x (x - 11) + 7 (x - 11) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 11 + 7 (x - 11) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 11 + 7 x + 7 \cdot - 11 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 11 + 7 x + 7 \cdot - 11 = 0$

Move $- 11$ to the left of $x$ .

$x^{2} - 11 \cdot x + 7 x + 7 \cdot - 11 = 0$

Multiply $7$ by $- 11$ .

$x^{2} - 11 x + 7 x - 77 = 0$

Add $- 11 x$ and $7 x$ .

$x^{2} - 4 x - 77 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 7, 11}$ is $y = x^{2} - 4 x - 77$ .

$y = x^{2} - 4 x - 77$

Step 5

Find the Quadratic Equation -7 , 11

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