Find a positive value of c so that thr trinomial is factorable.......................

3x^2 - 7x + c





c = ?

Find a positive value of c so that thr trinomial is factorable.......................
c=2 and c=4
Reply:In order for the trinomial to be factorable, it must be the case that its discriminant, b^2 - 4ac is a perfect square, and positive. With that said ... let's calculate b^2 - 4ac.





b^2 - 4ac =


(-7)^2 - 4(3)(c) =


49 - 12c





Therefore,





49 - 12c %26gt;= 0


-12c %26gt;= -49


c %26lt;= 49/12





Also, remember that c must be greater than 0 (as c must be a positive value).





49/12 is approximately 4.08 ... that means if





c %26lt;= 49/12, then c %26lt;= 4





Since c is positive (c %26gt; 0) and c %26lt;= 4, just test integers in between.





Test c = 1, c = 2, c = 3, c = 4.





If c = 1, then 49 - 12c = 49 - 12(1) = 49 - 12 = 37, which is not a perfect square. Reject.


If c = 2, then 49 - 12c = 49 - 12(2) = 49 - 24 = 25, which IS a perfect square.





c = 2 works.
Reply:Quadritic equation=3x2- 7x + c


y=3x2- 7x + c


Let's say that: A=3, B=7, C=?


Axis of symmetry:x=-b/2a


Substitution: x=(-7)/2(3)


x=-7/6


Plug-in the value of X:


y=3(-7/6)2 - 7(-7/6) + c


Simplify:49/12 + 49/6 +c


49 + 49/12 +c


y=98/12 +c


Let y=o, 12=98 + c


c=-86


Equation=3x2 - 7x - 86
Reply:b^2 -4ac =(-7)^2 -4(3)(c) =


49 -12c


c =0, c=2, c=4