Find the Quadratic Equation 4 , 6i , -6i

$4$ , $6 i$ , $- 6 i$

Step 1

$x = 4$ and $x = 6 i$ are the two real distinct solutions for the quadratic equation, which means that $x - 4$ and $x - 6 i$ are the factors of the quadratic equation.

$(x - 4) (x - 6 i) = 0$

Step 2

Expand $(x - 4) (x - 6 i)$ using the FOIL Method.

Apply the distributive property.

$x (x - 6 i) - 4 (x - 6 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 6 i) - 4 (x - 6 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 6 i) - 4 x - 4 (- 6 i) = 0$

Step 3

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- 6 i) - 4 x - 4 (- 6 i) = 0$

Multiply $- 6$ by $- 4$ .

$x^{2} + x (- 6 i) - 4 x + 24 i = 0$

Reorder factors in $x^{2} + x (- 6 i) - 4 x + 24 i$ .

$x^{2} - 6 x i - 4 x + 24 i = 0$

Step 4

The standard quadratic equation using the given set of solutions ${4, 6 i, - 6 i}$ is $y = x^{2} - 6 x i - 4 x + 24 i$ .

$y = x^{2} - 6 x i - 4 x + 24 i$

Step 5

Find the Quadratic Equation 4 , 6i , -6i

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