Question

State whether the following quadratic equations have two distinct real roots. Justicy your answer:
`x(1-x)-2=0`

Answer 1

Given equation is `x(1-x)-2=0`
`implies x-x^(2)-2=0`
`implies x^(2)-x=2=0`
On comparing with `ax^(2)-bx+c=0` we get
`a=1, b=-1` and `c=2`
`:.` Discriminant `D=b^(2)-4ac`
`=(-1)^(2)-4(1)(2)=1-8=-7lt0` i.e. `Dlt0`
Hence the equation `x(1-x)-2=0` has imaginary roots i.e. no real roots.