Question

Find the discriminant of the quadratic equation \( \sqrt{2}x^2 - x - \sqrt{2} = 0 \) and hence find the nature of the roots.

Hint:

Discriminant Calculation: \( D = b^2 - 4ac \) helps determine the nature of the roots.

Answer 1

Discriminant formula:
\[ D = b^2 - 4ac \] For \( \sqrt{2}x^2 - x - \sqrt{2} = 0 \),
\[ a = \sqrt{2}, \quad b = -1, \quad c = -\sqrt{2} \] \[ D = (-1)^2 - 4(\sqrt{2})(-\sqrt{2}) \] \[ = 1 - 4(2) \] \[ = 1 - 8 = 9 \] Since \( D>0 \), the roots are real and distinct.
Correct Answer: \( 9 \, \text{cm} \)