A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallon
1 answer:
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Answer:
.
Step-by-step explanation:
Let the smaller root to this equation be . The larger one will equal
.
By the factor theorem, this equation is equivalent to
, where
.
Expand this expression:
.
This equation and the one in the question shall differ only by the multiple of a non-zero constant. It will be helpful if that constant is equal to . That way, all constants in the two equations will be equal;
will be equal to
.
Compare this equation and the one in the question:
The coefficient of in the question is
(which is omitted.) The coefficient of
in this equation is
. If all corresponding coefficients in the two equations are equal to each other, these two coefficients shall also be equal to each other. Therefore
.
This equation will become:
.
Similarly, for the coefficient of ,
.
.
This equation will become:
.
is the value of the constant term of this quadratic equation.