Find the Quadratic Equation square root of 2 , 5i

$\sqrt{2}$ , $5 i$

Step 1

$x = \sqrt{2}$ and $x = 5 i$ are the two real distinct solutions for the quadratic equation, which means that $x - \sqrt{2}$ and $x - 5 i$ are the factors of the quadratic equation.

$(x - \sqrt{2}) (x - 5 i) = 0$

Step 2

Expand $(x - \sqrt{2}) (x - 5 i)$ using the FOIL Method.

Apply the distributive property.

$x (x - 5 i) - \sqrt{2} (x - 5 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 5 i) - \sqrt{2} (x - 5 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 5 i) - \sqrt{2} x - \sqrt{2} (- 5 i) = 0$

Step 3

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- 5 i) - \sqrt{2} x - \sqrt{2} (- 5 i) = 0$

Multiply $- 5$ by $- 1$ .

$x^{2} + x (- 5 i) - \sqrt{2} x + 5 \sqrt{2} i = 0$

Reorder factors in $x^{2} + x (- 5 i) - \sqrt{2} x + 5 \sqrt{2} i$ .

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

Step 4

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

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

Step 5

Find the Quadratic Equation square root of 2 , 5i

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