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

Algebra ->  Systems-of-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
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=x%5E2%2Bx%2B3 (notice how a=1, b=1 and c=3):

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

D=%281%29%5E2-4%2A1%2A3 Plug in a=1, b=1, c=3

D=1-4%2A1%2A3 Square 1 to get 1

D=1-12 Multiply -4*1*3 to get -12

D=-11 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 y=x%5E2%2Bx%2B3, we get

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx%2B3%29+

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