SOLUTION: please help me solve this a.calculate the value of the discriminant of x^2+x+3=0 b.by examining the sign of the discriminant in part a, how many x-intercepts would the graph of y

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: please help me solve this a.calculate the value of the discriminant of x^2+x+3=0 b.by examining the sign of the discriminant in part a, how many x-intercepts would the graph of y      Log On


   

Question 111671: please help me solve this
a.calculate the value of the discriminant of x^2+x+3=0
b.by examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+x+3 have?why?
this is under 1 problem. thank you tutor.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate the discriminant of:
y+=+x%5E2%2Bx%2B3
Since this quadratic equation is already in the standard form of: y+=+ax%5E2%2Bbx%2Bc and the discriminant is defined as: b%5E2-4ac, then:
b%5E2-4ac+=+1%5E2-4%281%29%283%29=1-12+=+-11
The discriminant is negative which means that the equation has two complex roots.
Why, because the discriminant is the quantity under the radical (square root sign) and the square root of a negative number is an imaginary number, so that the roots will be complex.
x+=+-0.5%2Bsqrt%2811%29i
x+=+-0.5-sqrt%2811%29i
Complex roots means that the graph of the equation (a parabola) never intercepts the x-axis, as shown by the graph below:
graph%28600%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B3%29