Question

State whether the following quadratic equations have two distinct real roots. Justify your answer.

`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0

Answer 1

The equation `sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0 has two real and distinct roots.

D = b² – 4ac

= `(-3/sqrt(2))^2 - 4(sqrt(2))(1/2)`

= `(9/2) - 2sqrt(2) > 0`

Hence, the roots are real and distinct.