Question 90545
Discriminant:

{{{D=b^2-4ac}}}


{{{D=4^2-4(1)(4)}}} Plug in a=1, b=4, a=4


{{{D=16-4(1)(4)}}} Square 4 to get 16 


{{{D=16-16)}}} Multiply {{{-4*4*1}}} to get {{{-16}}}


{{{D=0}}} Combine like terms



So a discriminant of zero means there is only one x-intercept


Remember, the quadratic formula is


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where the discriminant is {{{D=b^2-4ac}}}


So when you perform the quadratic formula, you would get


*[Tex \LARGE x=\frac{-4\pm sqrt{0}}{2}] Plug the discriminant and the given values into the formula


*[Tex \LARGE x=\frac{-4\pm0}{2}] Take the square root



So the expression breaks up to:


*[Tex \LARGE x=\frac{-4+0}{2}] or *[Tex \LARGE x=\frac{-4-0}{2}] 


*[Tex \LARGE x=\frac{-4}{2}] or *[Tex \LARGE x=\frac{-4}{2}] Add/subtract 0


*[Tex \LARGE x=-2] or *[Tex \LARGE x=-2] Simplify


So we can see that the two values are the same answer. So this means we only get one x-intercept