SOLUTION: How many solutions are there to the equation {{{f(x)=-0.2x^2+12x+11}}}? How do you know?

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Question 130493: How many solutions are there to the equation f%28x%29=-0.2x%5E2%2B12x%2B11? How do you know?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

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

D=b%5E2-4ac

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%5E2%2B12x%2B11 (notice how a=-0.2, b=12, and c=11)


D=b%5E2-4ac Start with the given equation

D=%2812%29%5E2-4%2A%28-0.2%29%2A%2811%29 Plug in a=-0.2, b=12, c=11

D=144-4%2A%28-0.2%29%2A%2811%29 Square 12 to get 144

D=144%2B8.8 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.