Find the Quadratic Equation Given the Roots 3 and 4

$3$ and $4$

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

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

Expand $(x - 3) (x - 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 3 (x - 4) = 0$

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 3$ by $- 4$ .

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

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

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

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

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

Find the Quadratic Equation Given the Roots 3 and 4

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