Find the Quadratic Equation Given the Roots 5 and -1

$5$ and $- 1$

Step 1

$x = 5$ and $x = - 1$ are the two real distinct solutions for the quadratic equation, which means that $x - 5$ and $x + 1$ are the factors of the quadratic equation.

$(x - 5) (x + 1) = 0$

Step 2

Expand $(x - 5) (x + 1)$ using the FOIL Method.

Apply the distributive property.

$x (x + 1) - 5 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 - 5 (x + 1) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 1 - 5 x - 5 \cdot 1 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 - 5 x - 5 \cdot 1 = 0$

Multiply $x$ by $1$ .

$x^{2} + x - 5 x - 5 \cdot 1 = 0$

Multiply $- 5$ by $1$ .

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

Subtract $5 x$ from $x$ .

$x^{2} - 4 x - 5 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${5, - 1}$ is $y = x^{2} - 4 x - 5$ .

$y = x^{2} - 4 x - 5$

Step 5

Find the Quadratic Equation Given the Roots 5 and -1

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