Find the Quadratic Equation 9i , -9i

$9 i$ , $- 9 i$

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify terms.

Combine the opposite terms in $x \cdot x + x (9 i) - 9 i x - 9 i (9 i)$ .

Reorder the factors in the terms $x (9 i)$ and $- 9 i x$ .

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

Subtract $9 i x$ from $9 i x$ .

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

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 9 i (9 i)$ .

Multiply $9$ by $- 9$ .

$x^{2} - 81 i i = 0$

Raise $i$ to the power of $1$ .

$x^{2} - 81 (i i) = 0$

Raise $i$ to the power of $1$ .

$x^{2} - 81 (i i) = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} - 81 i^{1 + 1} = 0$

Add $1$ and $1$ .

$x^{2} - 81 i^{2} = 0$

Rewrite $i^{2}$ as $- 1$ .

$x^{2} - 81 \cdot - 1 = 0$

Multiply $- 81$ by $- 1$ .

$x^{2} + 81 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${9 i, - 9 i}$ is $y = x^{2} + 81$ .

$y = x^{2} + 81$

Step 5

Find the Quadratic Equation 9i , -9i

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