x^2-2x+3=6

Question

write the equatin in standard form. Identify a,b and c

Answer 1

x²-2x+3=6, x²-2x-3=0 is the stadard quadratic form in which a=1, b=-2 and c=-3.

x²-2x-3=(x-3)(x+1) so x=3 or -1 are the roots, because x-3=0, that is, x=3; or x+1=0, that is, x=-1.

The roots can also be found using the quadratic formula:

x=(-b±√(b²-4ac))/2a=(2±√(4-4×1×(-3)))/(2×1),

x=(2±√(4+12))/2=(2±√16)/2=(2±4)/2 which is (2+4)/2=6/2=3 or (2-4)/2=-2/2=-1.

So x=3 or -1 as before.