Find the Quadratic Equation 1 , 9i , -9i

$1$ , $9 i$ , $- 9 i$

Step 1

$x = 1$ and $x = 9 i$ are the two real distinct solutions for the quadratic equation, which means that $x - 1$ and $x - 9 i$ are the factors of the quadratic equation.

$(x - 1) (x - 9 i) = 0$

Step 2

Expand $(x - 1) (x - 9 i)$ using the FOIL Method.

Apply the distributive property.

$x (x - 9 i) - 1 (x - 9 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 9 i) - 1 (x - 9 i) = 0$

Apply the distributive property.

$x \cdot x + x (- 9 i) - 1 x - 1 (- 9 i) = 0$

Step 3

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- 9 i) - 1 x - 1 (- 9 i) = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} + x (- 9 i) - x - 1 (- 9 i) = 0$

Multiply $- 9$ by $- 1$ .

$x^{2} + x (- 9 i) - x + 9 i = 0$

Reorder factors in $x^{2} + x (- 9 i) - x + 9 i$ .

$x^{2} - 9 x i - x + 9 i = 0$

Step 4

The standard quadratic equation using the given set of solutions ${1, 9 i, - 9 i}$ is $y = x^{2} - 9 x i - x + 9 i$ .

$y = x^{2} - 9 x i - x + 9 i$

Step 5

Find the Quadratic Equation 1 , 9i , -9i

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