Find the Quadratic Equation Given the Roots 3 , 4+i

$3$ , $4 + i$

$x = 3$ and $x = 4 + i$ are the two real distinct solutions for the quadratic equation, which means that $x - 3$ and $x - 4 + i$ are the factors of the quadratic equation.

$(x - 3) (x - 4 + i) = 0$

Expand $(x - 3) (x - 4 + i)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x \cdot - 4 + x i - 3 x - 3 \cdot - 4 - 3 i = 0$

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 + x i - 3 x - 3 \cdot - 4 - 3 i = 0$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x + x i - 3 x - 3 \cdot - 4 - 3 i = 0$

Multiply $- 3$ by $- 4$ .

$x^{2} - 4 x + x i - 3 x + 12 - 3 i = 0$

Subtract $3 x$ from $- 4 x$ .

$x^{2} + x i - 7 x + 12 - 3 i = 0$

The standard quadratic equation using the given set of solutions ${3, 4 + i}$ is $y = x^{2} + x i - 7 x + 12 - 3 i$ .

$y = x^{2} + x i - 7 x + 12 - 3 i$

Find the Quadratic Equation Given the Roots 3 , 4+i

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