Find the Quadratic Equation 2 , 3i , -3i

$2$ , $3 i$ , $- 3 i$

Step 1

$x = 2$ and $x = 3 i$ are the two real distinct solutions for the quadratic equation, which means that $x - 2$ and $x - 3 i$ are the factors of the quadratic equation.

$(x - 2) (x - 3 i) = 0$

Step 2

Expand $(x - 2) (x - 3 i)$ using the FOIL Method.

Apply the distributive property.

$x (x - 3 i) - 2 (x - 3 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 3 i) - 2 (x - 3 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 3 i) - 2 x - 2 (- 3 i) = 0$

Step 3

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- 3 i) - 2 x - 2 (- 3 i) = 0$

Multiply $- 3$ by $- 2$ .

$x^{2} + x (- 3 i) - 2 x + 6 i = 0$

Reorder factors in $x^{2} + x (- 3 i) - 2 x + 6 i$ .

$x^{2} - 3 x i - 2 x + 6 i = 0$

Step 4

The standard quadratic equation using the given set of solutions ${2, 3 i, - 3 i}$ is $y = x^{2} - 3 x i - 2 x + 6 i$ .

$y = x^{2} - 3 x i - 2 x + 6 i$

Step 5

Find the Quadratic Equation 2 , 3i , -3i

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