Find the Quadratic Equation - square root of 13 , square root of 13

$- \sqrt{13}$ , $\sqrt{13}$

$x = - \sqrt{13}$ and $x = \sqrt{13}$ are the two real distinct solutions for the quadratic equation, which means that $x + \sqrt{13}$ and $x - \sqrt{13}$ are the factors of the quadratic equation.

$(x + \sqrt{13}) (x - \sqrt{13}) = 0$

Expand $(x + \sqrt{13}) (x - \sqrt{13})$ using the FOIL Method.

Apply the distributive property.

$x (x - \sqrt{13}) + \sqrt{13} (x - \sqrt{13}) = 0$

Apply the distributive property.

$x \cdot x + x (- \sqrt{13}) + \sqrt{13} (x - \sqrt{13}) = 0$

Apply the distributive property.

$x \cdot x + x (- \sqrt{13}) + \sqrt{13} x + \sqrt{13} (- \sqrt{13}) = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- \sqrt{13}) + \sqrt{13} x + \sqrt{13} (- \sqrt{13})$ .

Reorder the factors in the terms $x (- \sqrt{13})$ and $\sqrt{13} x$ .

$x \cdot x - x \sqrt{13} + x \sqrt{13} + \sqrt{13} (- \sqrt{13}) = 0$

Add $- x \sqrt{13}$ and $x \sqrt{13}$ .

$x \cdot x + 0 + \sqrt{13} (- \sqrt{13}) = 0$

Add $x \cdot x$ and $0$ .

$x \cdot x + \sqrt{13} (- \sqrt{13}) = 0$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + \sqrt{13} (- \sqrt{13}) = 0$

Multiply $\sqrt{13} (- \sqrt{13})$ .

Raise $\sqrt{13}$ to the power of $1$ .

$x^{2} - (\sqrt{13} \sqrt{13}) = 0$

Raise $\sqrt{13}$ to the power of $1$ .

$x^{2} - (\sqrt{13} \sqrt{13}) = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} - {\sqrt{13}}^{1 + 1} = 0$

Add $1$ and $1$ .

$x^{2} - {\sqrt{13}}^{2} = 0$

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$x^{2} - {(13^{\frac{1}{2}})}^{2} = 0$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2} - 13^{\frac{1}{2} \cdot 2} = 0$

Combine $\frac{1}{2}$ and $2$ .

$x^{2} - 13^{\frac{2}{2}} = 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{2} - 13^{\frac{2}{2}} = 0$

Rewrite the expression.

$x^{2} - 13 = 0$

Evaluate the exponent.

$x^{2} - 1 \cdot 13 = 0$

Multiply $- 1$ by $13$ .

$x^{2} - 13 = 0$

The standard quadratic equation using the given set of solutions ${- \sqrt{13}, \sqrt{13}}$ is $y = x^{2} - 13$ .

$y = x^{2} - 13$

Find the Quadratic Equation - square root of 13 , square root of 13

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