Christy N. answered • 10/06/15

Making Math Make Sense

The quadratic formula is used when a quadratic equation (ax

^{2}+bx+c = 0) is un-factorable.If you were given, for example, the equation 2x

^{2 }- 5x - 3 = 0, you wouldn't need the quadratic formula. You could just factor the equation to (2x + 1) (x - 3)=0 and solve from there (by setting each binomial equal to zero and solving for your two solutions).Occasionally, however, you may be given a problem like 2x

^{2 }- 3x - 1 = 0 which would be considered un-factorable. In this case, you would use the quadratic formula X = (-b

^{+}_{- }sqrt b^{2}-4ac)/2amatching parts of

ax

^{2}+bx+c=0 and 2x

^{2 }-3x -1=0we find a = 2, b = -3, and c = -1

Now, just substitute those values into the quadratic formula and you have your answer(s)

x =[ -(-3)

^{+}_{- }sqrt of (-3)^{2 }-4 (2)(-1)]/2(2) x = [3

^{+}_{- }sqrt of 17]/4Technically, you could always use the quadratic formula (even on equations that are factorable...it would just be A LOT more work than necessary)