solving a quadratic equation
2x²-4x+3=0
We solve for possible values of x using the
following formula:
-b ± sqrt(b^2 - 4(a)(c))
x = --------------------------------
2(a)
-(-4) ± sqrt((-4)^2 - 4(2)(3))
x = --------------------------------------
2(2)
4 ± sqrt(16 - 24)
x = --------------------------------------
4
4 ± sqrt(-8)
x = --------------------------------------
4
We can stop right there. This part of
the formula, sqrt(b^2 - 4(a)(c)), is called
the discriminant. It will give us a clue as
to how many roots there are for the equation.
As you can see above, it reduced to a negative
number inside the square root operation. This
gives us imaginary numbers. Having a negative
discriminant means there are no values of x
where the graph of this equation crosses the
x-axis.