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 :
Start with the given equation
Plug in a=5, b=8, c=7
Square 8 to get 64
Multiply -4*5*7 to get -140
Combine 64 and -140 to get -76
Since the discriminant equals -76 (which is less than zero) , this means there are two complex solutions (ie there are no real solutions). Remember if the discriminant is less than zero, then the quadratic will have two complex solutions.
So the quadratic has no solutions
Notice if we graph , we can see that there are no real solutions. So this verifies our answer.
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