Question

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

Answer 1

Given equation is `(x+1)(x-2)+x=0`
`implies x^(2)+x-2x-2+x=0`
`implies x^(2)-2=0`
`implies x^(2)+0.x-2=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=1, b=0` and `c=-2`
`:.` Discriminant ` D=b^(2)-4ac=(0)^(2)-4(1)(-2)=0+8=8gt0`
Hence the equation `(x+1)(x-2)+x=0` has two distinct real roots.