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

Question 130493: How many solutions are there to the equation ? How do you know?

Answer by jim_thompson5910(35256) (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

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

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 (notice how a=-0.2, b=12, and c=11)

Start with the given equation

Plug in a=-0.2, b=12, c=11

Square 12 to get 144

Multiply -4*(-0.2)*(11) to get 8.8

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.

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