Find the Quadratic Equation Given the Roots 0 , -4 , square root of 3

$0$ , $- 4$ , $\sqrt{3}$

Step 1

$x = 0$ and $x = - 4$ are the two real distinct solutions for the quadratic equation, which means that $x - 0$ and $x + 4$ are the factors of the quadratic equation.

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

Step 2

Subtract $0$ from $x$ .

$x (x + 4) = 0$

Step 3

Apply the distributive property.

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

Step 4

Simplify the expression.

Multiply $x$ by $x$ .

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

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

$x^{2} + 4 x = 0$

Step 5

The standard quadratic equation using the given set of solutions ${0, - 4, \sqrt{3}}$ is $y = x^{2} + 4 x$ .

$y = x^{2} + 4 x$

Step 6

Find the Quadratic Equation Given the Roots 0 , -4 , square root of 3

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