Question

If a quadratic equation can be factored as (ax +b)(ex+d) = 0, what information do these factors provide about the graph of the equation?

Answer 1

Answer:

The 4th choice: The graph of the equation has roots at x = -b/a and x = -d/c

Explanation:

If we have an equation of the form

$(ax+b)(bx+c)=0$

then it must be that either

$(ax+b)=0$

or

$(bx+c)=0$

The first equation gives

$\begin{gathered} ax+b=0 \\ x=-\frac{b}{a} \end{gathered}$

and the second equation gives

$\begin{gathered} cx+d=0 \\ x=-\frac{d}{c} \end{gathered}$

Hence, the roots of the equation turn out to be

$x=-\frac{b}{a},x=-\frac{d}{c}$

Therefore, we conclude that the equation of the form (ax + b) (cx + d) tells us about the roots of the function, and hence, choice 4 is correct.