Question

How do you find the discriminant and how many solutions does `x^2+2x+7=0` have?

Answer 1

The equation is of the form `color(blue)(ax^2+bx+c=0` where:

`a=1, b=2, c=7`

The Disciminant is given by :
`Delta=b^2-4*a*c`
`= (2)^2-4*1*7`
`= 4-28=-24`

If `Delta=0` then there is only one solution.
(for `Delta>0` there are two solutions,
for `Delta<0` there are no real solutions)

As `Delta < 0`, this equation has NO REAL SOLUTIONS

• Note:
  The solutions are normally found using the formula
  `x=(-b+-sqrtDelta)/(2*a)`