Andrew M. answered • 09/20/17
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
3x2 - 6x + p
the discriminant is
b2-4ac = 36-12p
To have a double root (2 equal roots)the
root is -b/2a and the discriminant is zero:
36-12p = 0
12p = 36
p = 3
3x2 -6x + 3
3(x2 - 2x) + 3
3(x2 - 2x + 1) + 3 - 3
3(x-1)2
a = 3, h = 1, k = 0
Andrew M.
remember: (a+b)2=a2+2ab+b2
to complete the squuare of x2+nx
we need to take (n/2)2 and add that so we
have x2+ nx + (n/2)2 = (x + n/2)2
Example: Complete the square of x2 + 8x
(8/2) = 4, 42=16
x2+ 8x + 16 = (x+8/2)2 = (x+4)2
In this problem we were completing the square
of (x2-2x) so (-2/2)2 = (-1)2 = 1 ... so we add 1 to
x2 - 2x so that (x2 - 2x + 1) = (x-1)2
In order to maintain balance in the equation itself
if we add something we also subtract it. In changing
3(x2-2x) +3 to 3(x2-2x+1) + 3
we actually changed the total by +3 due to the 3
outside the parenthesis. Thus, we need to subtract
that 3 back out of the equation.
3(x2-2x)+3 = 3(x2-2x+1)+3-3 = 3(x-1)2
Report
09/21/17
Megan D.
3(x2 - 2 + 1) + 3 - 3
09/20/17