Find the Quadratic Equation 3-i , square root of 2

$3 - i$ , $\sqrt{2}$

Step 1

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

$(x - 3 - i) (x - \sqrt{2}) = 0$

Step 2

Expand $(x - 3 - i) (x - \sqrt{2})$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 3$ .

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

Multiply $- i (- \sqrt{2})$ .

Multiply $- 1$ by $- 1$ .

$x^{2} + x (- \sqrt{2}) - 3 x + 3 \sqrt{2} - i x + 1 i \sqrt{2} = 0$

Multiply $\sqrt{2}$ by $1$ .

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

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

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

Step 4

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

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

Step 5

Find the Quadratic Equation 3-i , square root of 2

Related Questions

Support LCMGCF.com by disabling your adblocker.