Question

understand

1. reason one solution of a quadratic equation is 6. what do you know about the quadratic equation? what are two ways you would know if a quadratic equation could have this solution?
2. ...

Explanation:

1. First, if 8 is a solution of a quadratic equation $ax^2+bx+c=0$, substituting $x=8$ satisfies the equation, so $64a + 8b + c = 0$. Also, the quadratic can be factored to include $(x-8)$ as a factor, meaning it can be written as $(x-8)(mx+n)=0$ where $m

eq0$.

1. Two ways to verify if 8 is a solution:

• Substitution: Plug $x=8$ into the quadratic equation. If the result equals 0, 8 is a solution.
• Factoring: If the quadratic can be factored to $(x-8)(\text{linear term})=0$, then 8 is a root (solution) by the zero product property.

Answer:

1. We know:

• Substituting $x=8$ into the quadratic equation $ax^2+bx+c=0$ gives $64a + 8b + c = 0$.
• The quadratic equation can be written in factored form as $(x-8)(kx + d) = 0$ where $k

eq 0$.

1. Two ways to check if 8 is a solution:

• Substitute $x=8$ into the equation; if it equals 0, 8 is a solution.
• Factor the quadratic; if $(x-8)$ is a factor, 8 is a solution.