Andrew M. answered • 07/04/15

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

From ax

^{2}+ bx + c which is a quadratic equation graphing to a parabolaSolve for the determinant , the part under the square root... b

^{2}-4acfrom the quadratic equation x =[ -b ± √(b

^{2}-4ac)]/2aif b

^{2}-4ac is positive we have 2 real rootsif b

^{2}-4ac = 0 we have 1 real rootif b

^{2}-4ac is negative we have 2 imaginary roots which are complex conjugatesIn this case we have x

^{2}-12x+ 36a = 1 b = -12 c =36

b

^{2}-4ac = (-12)^{2}-4(1)36 = 144 - 144 = 0Since the determinant = 0 we will have only one real root (x=6 as Maria stated)