Question

How do you find the discriminant and how many and what type of solutions does `y = –2x^2 + x – 3` have?

Answer 1

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

`a=-2, b=1, c=-3`

The Disciminant is given by :
`Delta=b^2-4*a*c`
`= (1)^2-(4*(-2)*(-3))`
`= 1-24=-23`

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 = -23`, this equation has NO REAL SOLUTIONS

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

As `Delta = -23`, `x = (-(1)+-sqrt(-23))/(2*-2) = (-(1)+-sqrt(-23))/-4`