{{ item.displayTitle }}

No history yet!

Student

Teacher

{{ item.displayTitle }}

{{ item.subject.displayTitle }}

{{ searchError }}

{{ courseTrack.displayTitle }} {{ statistics.percent }}% Sign in to view progress

{{ printedBook.courseTrack.name }} {{ printedBook.name }}
Let's write the equation in the form $f(x)=a(x−p)(x−q).$ The leading coefficient $a$ can be any non-zero real number and $p$ and $q$ are the zeros of the function. Since the roots are $8$ and $12,$ our equation can be written as follows.
$f(x)=a(x−8)(x−12) $
Note that *any* equation in the above form will have roots $8$ and $11,$ regardless the value of $a.$ For simplicity, let's set $a=1.$
Note that there are infinitely many equations that satisfy the given condition. This is just one of them.

$f(x)=a(x−8)(x−12)$

Substitute$a=1$

$f(x)=1(x−8)(x−12)$

Simplify right-hand side

IdPropMultIdentity Property of Multiplication

$f(x)=(x−8)(x−12)$

DistrDistribute $(x−8)$

$f(x)=x(x−8)−12(x−8)$

DistrDistribute $x$

$f(x)=x_{2}−8x−12(x−8)$

DistrDistribute $-12$

$f(x)=x_{2}−8x−12x+96$

SubTermSubtract term

$f(x)=x_{2}−20x+96$