SOLUTION: ok this one I really do not understand becuase they do not give me a value for x or anything. Part A) Calculate the value of the discriminant of x^2+x+3=0 Part B) by examinin

Question 128657: ok this one I really do not understand becuase they do not give me a value for x or anything.
Part A) Calculate the value of the discriminant of x^2+x+3=0
Part B) by examining teh sign of the discriminant in part a, how many x-intercepts would the graph of y = x^2+x+3 have? Why?
I know that to get the discrimant the equation is b^2 - 4ac, and that if the discriminant is positive the the solutions will be real numbers, and if it is a negative you will have two complex solutions. but how do I solve this if I do not know what the value of b is or the value of A and C
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 , and ):

Start with the given equation

Plug in a=1, b=1, c=3

Square 1 to get 1

Multiply -4*1*3 to get -12

Combine 1 and -12 to get -11

Since the discriminant equals -11 (which is less than zero) , this means there are two complex solutions.

Notice if we graph , we get

and we can see that there are two complex solutions. So this visually verifies our answer.

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