Question

The value of the discriminant of the equation, `x^2 - (sqrt(2) + 1)x + sqrt(2) = 0` is ______.

Options

• `3 + 2sqrt(2)`

• `1 - 2sqrt(2)`

• `3 - 2sqrt(2)`

• `2 - sqrt(2)`

Answer 1

The value of the discriminant of the equation, `x^2 - (sqrt(2) + 1)x + sqrt(2) = 0` is `underlinebb(3 - 2sqrt(2))`.

Explanation:

For ax² + bx + c = 0 

Here a = 1, b = `-(sqrt(2) + 1)`, c = `sqrt(2)`.

Discriminant D = b² – 4ac 

= `(sqrt(2) + 1)^2 - 4 xx 1 xx sqrt(2)` 

= `(3 + 2sqrt(2)) - 4sqrt(2)` 

= `3 - 2sqrt(2)`