Find the Quadratic Equation -5 , 7

$- 5$ , $7$

Step 1

$x = - 5$ and $x = 7$ are the two real distinct solutions for the quadratic equation, which means that $x + 5$ and $x - 7$ are the factors of the quadratic equation.

$(x + 5) (x - 7) = 0$

Step 2

Expand $(x + 5) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) + 5 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 5 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 5 x + 5 \cdot - 7 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 + 5 x + 5 \cdot - 7 = 0$

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

$x^{2} - 7 \cdot x + 5 x + 5 \cdot - 7 = 0$

Multiply $5$ by $- 7$ .

$x^{2} - 7 x + 5 x - 35 = 0$

Add $- 7 x$ and $5 x$ .

$x^{2} - 2 x - 35 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 5, 7}$ is $y = x^{2} - 2 x - 35$ .

$y = x^{2} - 2 x - 35$

Step 5

Find the Quadratic Equation -5 , 7

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