Question

one solution of a quadratic equation is 8. what do you know about the quadratic equation? what are two ways you would know if a quadratic equation could have this solution?
choose the correct answer below
a. the expression $x - 8$ must be a factor. to know this, divide both sides by 8 and solve for x to check if the solution is 0, or factor the equation to see if $x - 8$ is a factor
b. the expression $x - 8$ must be a factor. to know this, substitute 8 into the quadratic equation and see if it checks, or factor the equation to see if $x - 8$ is a factor
c. the expression $x + 8$ must be a factor. to know this, substitute 8 into the quadratic equation and see if it checks, or factor the equation to see if $x + 8$ is a factor
d. the expression $x + 8$ must be a factor. to know this, divide both sides by 8 and solve for x to check if the solution is 0, or factor the equation to see if $x + 8$ is a factor

Explanation:

1. If $x=8$ is a solution of a quadratic equation $f(x)=0$, then by the Factor Theorem, $(x-8)$ is a factor of the quadratic polynomial $f(x)$.
2. To verify that 8 is a solution:

• Substitute $x=8$ into the equation; if the result is 0, it is a valid solution.
• Factor the quadratic equation; if $(x-8)$ is one of the factors, then $x=8$ is a solution.

1. Options A, C, and D contain incorrect factors ($x+8$) or invalid verification steps, so they are not correct.

Answer:

B. The expression $x - 8$ must be a factor. To know this, substitute 8 into the quadratic equation and see if it checks, or factor the equation to see if $x - 8$ is a factor