Find the Quadratic Equation Given the Roots 0 , 5 , -5+ square root of 8

$0$ , $5$ , $- 5 + \sqrt{8}$

Step 1

$x = 0$ and $x = 5$ are the two real distinct solutions for the quadratic equation, which means that $x - 0$ and $x - 5$ are the factors of the quadratic equation.

$(x - 0) (x - 5) = 0$

Step 2

Subtract $0$ from $x$ .

$x (x - 5) = 0$

Step 3

Apply the distributive property.

$x \cdot x + x \cdot - 5 = 0$

Step 4

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 = 0$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 x = 0$

Step 5

The standard quadratic equation using the given set of solutions ${0, 5, - 5 + \sqrt{8}}$ is $y = x^{2} - 5 x$ .

$y = x^{2} - 5 x$

Step 6

Find the Quadratic Equation Given the Roots 0 , 5 , -5+ square root of 8

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