Question

Find the discriminant of the quadratic equation \( 9x^2 - 6x + 1 = 0 \) and hence find the nature of the roots.

Hint:

If \( \Delta>0 \), roots are real and distinct; if \( \Delta = 0 \), roots are real and equal; if \( \Delta<0 \), roots are imaginary.

Answer 1

The discriminant of a quadratic equation \( ax^2 + bx + c = 0 \) is given by:
\[ \Delta = b^2 - 4ac. \] For \( 9x^2 - 6x + 1 = 0 \):
\[ \Delta = (-6)^2 - 4(9)(1) = 36 - 36 = 0. \] Since \( \Delta = 0 \), the roots are real and equal.