Algebra Examples

$(2, \infty)$

Step 1

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

$(x - 2) (x + - \infty) = 0$

Step 2

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

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Apply the distributive property.

$x (x + - \infty) - 2 (x + - \infty) = 0$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + x + - \infty - 2 x - 2 + - \infty = 0$

A non-zero constant times infinity is infinity.

$x^{2} + x + - \infty - 2 x + \infty = 0$

Step 4

The standard quadratic equation using the given set of solutions ${2, \infty}$ is $y = x^{2} + x + - \infty - 2 x + \infty$ .

$y = x^{2} + x + - \infty - 2 x + \infty$

Step 5