Find the Quadratic Equation Given the Roots 4 , - square root of 5

$4$ , $- \sqrt{5}$

Step 1

$x = 4$ and $x = - \sqrt{5}$ are the two real distinct solutions for the quadratic equation, which means that $x - 4$ and $x + \sqrt{5}$ are the factors of the quadratic equation.

$(x - 4) (x + \sqrt{5}) = 0$

Step 2

Expand $(x - 4) (x + \sqrt{5})$ using the FOIL Method.

Apply the distributive property.

$x (x + \sqrt{5}) - 4 (x + \sqrt{5}) = 0$

Apply the distributive property.

$x \cdot x + x \sqrt{5} - 4 (x + \sqrt{5}) = 0$

Apply the distributive property.

$x \cdot x + x \sqrt{5} - 4 x - 4 \sqrt{5} = 0$

Step 3

Multiply $x$ by $x$ .

$x^{2} + x \sqrt{5} - 4 x - 4 \sqrt{5} = 0$

Step 4

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

$y = x^{2} + x \sqrt{5} - 4 x - 4 \sqrt{5}$

Step 5

Find the Quadratic Equation Given the Roots 4 , - square root of 5

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