Question 130493
If you look at part c), you'll see that there are two solutions. 



To figure out how many solutions a quadratic will have, simply use the discriminant


From the quadratic formula

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


the discriminant consists of all of the terms in the square root. So the discriminant is


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


the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.



Now let's find the discriminant for {{{y=-0.2x^2+12x+11}}} (notice how a=-0.2, b=12, and c=11)



{{{D=b^2-4ac}}} Start with the given equation


{{{D=(12)^2-4*(-0.2)*(11)}}} Plug in a=-0.2, b=12, c=11


{{{D=144-4*(-0.2)*(11)}}} Square 12 to get 144


{{{D=144+8.8}}} Multiply -4*(-0.2)*(11) to get 8.8


{{{D=152.8}}} Add



Since the discriminant equals 152.8  (which is greater than zero) , this means  there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.