Question

How do you find the discriminant and how many and what type of solutions does `4x^2-2x+1=0` have?

Answer 1

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

`a=4, b=-2, c=1`

The Disciminant is given by :
`Delta=b^2-4*a*c`
`= (-2)^2-(4*4*1)`
`= 4-16=-12`

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 = -12`, this equation has NO REAL SOLUTIONS

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

Substituting the value of `Delta` will give us 2 imaginary roots/solutions.