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

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=-(b)/(a) \end{gathered}`

and the second equation gives

`\begin{gathered} cx+d=0 \\ x=-(d)/(c) \end{gathered}`

Hence, the roots of the equation turn out to be

`x=-(b)/(a),x=-(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.