Question

How do you find the discriminant and how many and what type of solutions does `y = 4x^2 – 12x + 12` have?

Answer 1

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

`a=4, b=-12, c=12`

The Disciminant is given by :
`Delta=b^2-4*a*c`
`= (-12)^2-(4*(4)*12)`
`= 144-192=4+252=-48`

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 = -48`, this equation has NO REAL SOLUTIONS

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

As `Delta = -48`, `x = (-(-12)+-sqrt(-48))/(2*4) = (12+-sqrt(-48))/8`